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Probability, SM-Bank 058 MC

A bag of balls contains only blue and white balls.

Jimoen picks one ball from the bag.

What is the chance the ball is white?

  1. \(\dfrac{2}{7}\)
  2. \(\dfrac{1}{3}\)
  3. \(\dfrac{2}{5}\)
  4. \(\dfrac{5}{7}\)
Show Answers Only

\(D\)

Show Worked Solution
\(P\text{(white)}\) \(=\dfrac{\text{Number of white balls}}{\text{Total number of balls}}\)
  \(=\dfrac{5}{7}\)

\(\Rightarrow D\)

Probability, SM-Bank 057 MC

Blinky is blowing up balloons for a birthday party.

The number of blown up balloons of each colour is recorded in the table below.

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Colour} \rule[-1ex]{0pt}{0pt} & \textbf{Number of Balloons} \\
\hline
\rule{0pt}{2.5ex} \text{white} \rule[-1ex]{0pt}{0pt} & 11 \\
\hline
\rule{0pt}{2.5ex} \text{purple} \rule[-1ex]{0pt}{0pt} & 7 \\
\hline
\rule{0pt}{2.5ex} \text{orange} \rule[-1ex]{0pt}{0pt} & 6 \\
\hline
\rule{0pt}{2.5ex} \text{yellow} \rule[-1ex]{0pt}{0pt} & 9 \\
\hline
\end{array}

Blinky picks one balloon without looking and gives it to the first person who arrives at the party.

What is the chance it is white?

  1. \(\dfrac{1}{11}\)
  2. \(\dfrac{1}{27}\)
  3. \(\dfrac{1}{2}\)
  4. \(\dfrac{1}{3}\)
Show Answers Only

\(D\)

Show Worked Solution
\(P\text{(white)}\) \(=\dfrac{\text{Number of white balloons}}{\text{Total number of balloons}}\)
  \(=\dfrac{11}{11+7+6+9}\)
  \(=\dfrac{11}{33}\)
  \(=\dfrac{1}{3}\)

\(\Rightarrow D\)

Probability, SM-Bank 056

Marie has a bag containing various coloured balls.

Marie grabs a coloured ball from the bag and records the colour.

She then puts the ball back into the bag and repeats this process a number of times.

 
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Orange} \rule[-1ex]{0pt}{0pt} & \ \ \text{Blue}\ \ \rule[-1ex]{0pt}{0pt} & \ \ \text{Red}\ \ \rule[-1ex]{0pt}{0pt} & \text{Green} \rule[-1ex]{0pt}{0pt} \ & \text{White} \rule[-1ex]{0pt}{0pt} & \text{Black} \rule[-1ex]{0pt}{0pt} & \text{Yellow} \rule[-1ex]{0pt}{0pt} \\
\hline
13 & 20 & 18 & 9 & 12 & 14 & 10\\
\hline
\end{array} 

Using the table, what is the probability that the next ball picked out by Marie will be yellow? (2 marks)

Show Answers Only

\(\dfrac{1}{6}\)

Show Worked Solution
\(P \text{(white)}\) \(=\dfrac{\text{Number of white}}{\text{Total number of selections}}\)
  \(=\dfrac{12}{13 + 20 + 18 + 9 + 12 + 14 + 10}\)
  \(=\dfrac{12}{96}\)
  \(=\dfrac{1}{8}\)

Probability, SM-Bank 055

Jackson spins a wheel with 5 different coloured sections and records which colour it lands on each time.

He repeats the process multiple times.

The table below shows the results.
 

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \text{White} \rule[-1ex]{0pt}{0pt} & \text{Yellow} \rule[-1ex]{0pt}{0pt} & \ \ \text{Red}\ \ \rule[-1ex]{0pt}{0pt} & \ \text{Blue} \rule[-1ex]{0pt}{0pt}\ \ & \text{Green} \rule[-1ex]{0pt}{0pt} \\
\hline
40 & 26 & 36 & 28 & 38\\
\hline
\end{array} 

Using the table, what is the probability that the next spin will be Blue?  (2 marks)

Show Answers Only

\(\dfrac{1}{6}\)

Show Worked Solution
\(P \text{(Blue)}\) \(=\dfrac{\text{Number of blue}}{\text{Total number of throws}}\)
  \(=\dfrac{28}{40 + 26 + 36 + 28 + 38}\)
  \(=\dfrac{28}{168}\)
  \(=\dfrac{1}{6}\)

Probability, SM-Bank 054

The two spinners shown are used in a game.

2UG 2011 26a1

Each arrow is spun once. The score is the total of the two numbers shown by the arrows.
A table is drawn up to show all scores that can be obtained in this game.

2UG 2011 26a2

  1. What is the value of \(X\) in the table?  (1 mark)
  2. What is the probability of obtaining a score less than 4?  (1 mark)
  3. On Spinner \(B\), a 2 is obtained. What is the probability of obtaining a score of 3?  (1 mark)
Show Answers Only

a.    \(5\)

b.    \(\dfrac{1}{2}\)

c.    \(\dfrac{2}{3}\)

Show Worked Solution

a.    \(X=2+3=5\)

b.    \(P\text{(score < 4)}=\dfrac{6}{12}=\dfrac{1}{2}\)

c.   \(\text{Given Spinner } B =2\)

\(\text{Possible spins }\rightarrow\ (2 , 1), (2 , 1), (2 , 3)\)

\(P\text{(score = 3)}=\dfrac{2}{3}\)

Probability, SM-Bank 053

Two unbiased dice,  \(A\)  and  \(B\), with faces numbered  \(1\),  \(2\),  \(3\),  \(4\),  \(5\) and  \(6\) are rolled.

The numbers on the uppermost faces are noted. This table shows all the possible outcomes.

 
\begin{align}
\textbf{Die B } \
\begin{array}{c }
\textbf{Die A } \\
\begin{array}{c|c|c|c|c|c|c}
\ & 1 & 2 & 3 & 4 & 5 & 6  \\
\hline
\ 1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6  \\
\hline
\ 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6  \\
\hline
\ 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6  \\
\hline
\ 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6  \\
\hline
\ 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6  \\
\hline
\ 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6  \\
\end{array}
\end{array}
\end{align}

 

A game is played where the difference between the highest number showing and the lowest number showing on the uppermost faces is calculated.

What is the probability that the difference between the numbers showing on the uppermost faces of the two dice is one?   (2 marks)

Show Answers Only

\(\dfrac{5}{18}\)

Show Worked Solution

\begin{align}
\textbf{Die B } \
\begin{array}{c }
\textbf{Die A } \\
\begin{array}{c|c|c|c|c|c|c}
\ & 1 & 2 & 3 & 4 & 5 & 6  \\
\hline
\ 1 & 1,1 & \colorbox{lightblue}{1,2} & 1,3 & 1,4 & 1,5 & 1,6  \\
\hline
\ 2 & \colorbox{lightblue}{2,1} & 2,2 & \colorbox{lightblue}{2,3} & 2,4 & 2,5 & 2,6  \\
\hline
\ 3 & 3,1 & \colorbox{lightblue}{3,2} & 3,3 & \colorbox{lightblue}{3,4} & 3,5 & 3,6  \\
\hline
\ 4 & 4,1 & 4,2 & \colorbox{lightblue}{4,3} & 4,4 & \colorbox{lightblue}{4,5} & 4,6  \\
\hline
\ 5 & 5,1 & 5,2 & 5,3 & \colorbox{lightblue}{5,4} & 5,5 & \colorbox{lightblue}{5,6}  \\
\hline
\ 6 & 6,1 & 6,2 & 6,3 & 6,4 & \colorbox{lightblue}{6,5} & 6,6  \\
\end{array}
\end{array}
\end{align}

 

\(\text{# Outcomes with a difference of 1}\)

\(=10\)

\(\therefore\ P \text{(diff of 1)}=\dfrac{10}{36}=\dfrac{5}{18}\)

Probability, SM-Bank 052

A random sample of people were asked what is their favourite winter sport.

The table below recorded the results.
 

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Sport} \rule[-1ex]{0pt}{0pt} & \textbf{Number of People} \\
\hline
\rule{0pt}{2.5ex} \text{Netball} \rule[-1ex]{0pt}{0pt} & \text{49} \\
\hline
\rule{0pt}{2.5ex} \text{Aussie Rules} \rule[-1ex]{0pt}{0pt} & \text{19} \\
\hline
\rule{0pt}{2.5ex} \text{Rugby League} \rule[-1ex]{0pt}{0pt} & \text{135} \\
\hline
\rule{0pt}{2.5ex} \text{Ice Hockey} \rule[-1ex]{0pt}{0pt} & \text{13} \\
\hline
\end{array}

Using the data from the survey, predict how many people would choose rugby league if 2000 people were surveyed.  (2 marks)

Show Answers Only

\(1250\)

Show Worked Solution

\(\text{Total people surveyed}\)

\(=49+19+135+13\)

\(=216\)

\(\therefore\ \text{Predicted number to choose rugby league}\)

\(=P\text{(Rugby League)}\times 2000\)

\(=\dfrac{135}{216}\times 2000\)

\(=1250\)

Probability, SM-Bank 051

In any standard six-sided dice, the sum of the opposite faces is 7.

Milo rolls 3 dice and the total of the top faces is 5.

What is the sum of the three opposite faces?  (2 marks)

Show Answers Only

\(16\)

Show Worked Solution

\(\text{Sum of 3 top faces + 3 opposite}\)

\(=3\times 7\)

\(=21\)

\(\therefore\ \text{Sum of 3 opposite faces}\)

\(=21-5\)

\(=16\)

Probability, SM-Bank 050

Mandy surveyed all year 7 students about their favourite flavour of milkshake.
 

 
Which flavour did 4 out of 10 year 7 students choose as their favourite?  (2 marks)

Show Answers Only

\(\text{Vanilla}\)

Show Worked Solution
\(\text{Total students}\) \(=75+100+35+40\)
  \(=250\)

 
\(\text{If 4 out of 10 students chose a certain flavour,}\)

\(\text{Number of students}\)

\(=\dfrac{4}{10}\times 250\)

\(=100\)
 

\(\therefore\ \text{4 out of 10 students choose Vanilla.}\)

Probability, SM-Bank 049

Maxi and Jim are playing a dice game.

They have two standard 6-sided dice.

One of the die is white and the other is grey.

Maxi needs to roll a total of 11 to win.

There are two different ways she can roll a total of 11 as shown.
 
 

Jim has to roll a 6 to win.

How many different ways can Jim roll a total of 6?  (1 mark)

Show Answers Only

\(\text{5 different ways.}\)

Show Worked Solution

\(\text{The table below shows the ways a sum of 6 can be rolled.}\)

\(\therefore\ \text{5 different ways.}\)

Probability, SM-Bank 048

Rachel has a bag that contains 6 blue and 4 green balls.

She selects one ball at random and records its colour. The ball is then put back into the bag.

Rachel does this 50 times.

How many times should Rachel expect to select a green ball from the bag?  (2 marks)

Show Answers Only

\(20\)

Show Worked Solution

\(P\text{(picking green)}=\dfrac{4}{10}=\dfrac{2}{5}\)

\(\therefore\ \text{Expected green balls}\) \(=\dfrac{2}{5}\times 50\)
  \(=20\)

Probability, SM-Bank 047

Sharon made 24 milkshakes at her nephew's birthday party. The milkshakes were either vanilla or chocolate.

All the milkshakes were served in an aluminium cup and looked the same.

Murray took one milkshake and had a 1 in 8 chance of taking a vanilla milkshake.

How many chocolate milkshakes did Sharon make?  (2 marks)

Show Answers Only

\(21\)

Show Worked Solution

\(\text{Number of vanilla milkshakes}\)

\(=\dfrac{1}{8}\times 24\)

\(=3\)
 

\(\therefore\ \text{Number of chocolate}\)

\(=24-3\)

\(=21\)

Probability, SM-Bank 046 MC

A standard six-sided dice is rolled once.

What is the probability that the number on the top face is a factor of 4?

  1. \(\dfrac{5}{6}\)
  2. \(\dfrac{1}{2}\)
  3. \(\dfrac{1}{3}\)
  4. \(\dfrac{1}{6}\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Factors of 4 are: 1, 4, 2}\)

\(\therefore\ P\text{(factor of 4)}\) \(=\dfrac{3}{6}\)
  \(=\dfrac{1}{2}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 045

Albert has 50 marbles in a bag.

He records the colour of each marble in the table below.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Marble} \rule[-1ex]{0pt}{0pt} & \textbf{Number of Marbles} \\
\hline
\rule{0pt}{2.5ex} \text{Blue} \rule[-1ex]{0pt}{0pt} & \text{20} \\
\hline
\rule{0pt}{2.5ex} \text{Red} \rule[-1ex]{0pt}{0pt} & \text{12} \\
\hline
\rule{0pt}{2.5ex} \text{Orange} \rule[-1ex]{0pt}{0pt} & \text{4} \\
\hline
\rule{0pt}{2.5ex} \text{White} \rule[-1ex]{0pt}{0pt} & \text{?} \\
\hline
\rule{0pt}{2.5ex} \textbf{TOTAL} \rule[-1ex]{0pt}{0pt} & \textbf{50} \\
\hline
\end{array}

  1. What percentage of the marbles are white?  (1 mark)
  2. If Albert draws a marble from the bag at random, what is the probability that the marble will be orange or white? Give your answer as a fraction in simplest form.  (2 marks)
Show Answers Only

a.    \(28\%\)

b.    \(\dfrac{9}{25}\)

Show Worked Solution

a.    \(\text{Number of white marbles}\)

 \(=50-(20+12+4)\)

\(=14\)

\(\therefore\ \%\text{ white}\) \(=\dfrac{14}{50}\times 100\)
  \(=28\%\)
b.    \(P\text{(Orange or white)}\) \(=\dfrac{\text{number orange and white}}{\text{total number of marbles}}\)
    \(=\dfrac{4+14}{50}=\dfrac{18}{50}\)
    \(=\dfrac{9}{25}\)

Probability, SM-Bank 044

Ronald rolled a standard dice 80 times.

He recorded if an odd or even number was rolled, each time, and wrote the results in the table below.
 

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{} \rule[-1ex]{0pt}{0pt} & \textbf{Number of times} \\
\hline
\rule{0pt}{2.5ex} \textbf{Odd} \rule[-1ex]{0pt}{0pt} & \text{33} \\
\hline
\rule{0pt}{2.5ex} \textbf{Even} \rule[-1ex]{0pt}{0pt} & \text{47} \\
\hline
\end{array}

What is the difference between the expected number of odd rolls and the actual number recorded?  (2 marks)

Show Answers Only

\(7\)

Show Worked Solution

\(\text{50% = the probability of an odd roll.}\)

\(\text{Expected odd rolls}\)

\(=50\%\times 80\)

\(=40\)
 

\(\therefore\ \text{Difference}\) \(=40-33\)
  \(=7\)

Probability, SM-Bank 043 MC

Aurora rolls a standard six-sided die.

Which of the following events has a probability of less than 0.5?

  1. rolling a number greater than 1
  2. rolling an odd number
  3. rolling a number less than 5
  4. rolling a number greater than or equal to 6
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Considering each option}\)

\(\text{Option A: }\ P\text{(number > 1)}=\dfrac{5}{6}=0.83\)

\(\text{Option B: }\ P\text{(odd number)}=\dfrac{3}{6}=0.5\)

\(\text{Option C: }\ P\text{(number < 5)}=\dfrac{4}{6}=0.67\)

\(\text{Option D: }\ P\text{(number}\geq 6)=\dfrac{1}{6}=0.17\ \checkmark\)

 
\(\Rightarrow D\)

Probability, SM-Bank 042

Archer did a survey of his class, asking everyone what their favourite ice cream flavour is.

This table below shows the results.
 

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Flavour} \rule[-1ex]{0pt}{0pt} & \textbf{Number of Classmates} \\
\hline
\rule{0pt}{2.5ex} \text{Chocolate} \rule[-1ex]{0pt}{0pt} & 14\\
\hline
\rule{0pt}{2.5ex} \text{Vanilla} \rule[-1ex]{0pt}{0pt} & 17 \\
\hline
\rule{0pt}{2.5ex} \text{Strawberry} \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\end{array}

What is the probability that a randomly selected classmate's favourite flavour is chocolate?

Round your answer to the nearest hundredth.  (2 marks)

Show Answers Only

\(0.39\)

Show Worked Solution
\(P\text{(likes chocolate)}\) \(=\dfrac{\text{number who chose chocolate}}{\text{total number of classmates}}\)
  \(=\dfrac{14}{14+17+8}\)
  \(=\dfrac{14}{39}\)
  \(=0.358\dots\)
  \(\approx 0.36\ \text{(nearest hundredth)}\)

Probability, SM-Bank 041

Claire baked 18 cookies.

She baked equal numbers of chocolate chip, macadamia nut and plain cookies.

Claire randomly picked one of the cookies.

  1. What are the chances it was chocolate chip or plain?  (1 mark)
  2. Claire's brother ate a macadamia nut cookie. What are the chances that the next cookie Claire randomly selects is macadamia nut or plain?  (2 marks)
Show Answers Only

a.    \(\dfrac{2}{3}\)

b.    \(\dfrac{11}{17}\)

Show Worked Solution
a.    \(P\text{(choosing chocolate chip or plain)}\) \(=\dfrac{\text{number of chocolate chip and plain}}{\text{total number of cookies}}\)
    \(=\dfrac{12}{18}\)
    \(=\dfrac{2}{3}\)

 

b.    \(P\text{(choosing macadamia or plain)}\) \(=\dfrac{\text{number of macadamia and plain}}{\text{total number of cookies}}\)
    \(=\dfrac{5+6}{17}\)
    \(=\dfrac{11}{17}\)

Probability, SM-Bank 040

Elodie turns over the cards below and mixes them up.
 

 
She selects one at random.

  1. What is the chance of Elodie selecting a 2 of spades?  (1 mark)
  2. What is the chance of Elodie selecting a card that does not have an even number of it?  (1 mark)
Show Answers Only

a.    \(\dfrac{2}{5}\)

b.    \(\dfrac{3}{10}\)

Show Worked Solution

a.    \(P\text{(selecting a 2 of spades)}\)

\(=\dfrac{4}{10}\)

\(=\dfrac{2}{5}\)

b.    \(P\text{(selecting not even)}\) \(=P\text{(selecting odd)}\)
    \(=\dfrac{3}{10}\)

 

Probability, SM-Bank 039 MC

Nev spins the arrow 50 times.
 

 
Which table is most likely to show his result?

Show Answers Only

\(B\)

Show Worked Solution

\(\text{One strategy:}\)

\(\text{X should be worth }\dfrac{2}{5}\ \text{(20 spins),}\)

\(\rightarrow\ \text{Eliminate the first and last options.}\)

\(\text{The other relative sizes require the answer to be:}\)

\(\Rightarrow B\)

Probability, SM-Bank 038 MC

Bryce has a bag of marbles. 80% of his marbles are red.

Bryce takes a yellow marble from his bag and loses it in a game.

If he takes another marble from the bag without looking, what are the chances it is red?

  1. greater than 80%
  2. equal to 80%
  3. less than 80%
  4. there is not enough information to predict the chance
Show Answers Only

\(A\)

Show Worked Solution

\(\text{There will be greater than 80% chance}\)

\(\text{because there are the same amount of }\)

\(\text{red marbles to be chosen but 1 less}\)

\(\text{marble in the bag.}\)

 
\(\Rightarrow A\)

Probability, SM-Bank 037

A school canteen has two different types of sandwiches.

There are 14 chicken sandwiches and 11 vegemite sandwiches.

The canteen sells one sandwich to each of the first five students in line at lunch time.

The table shows the type of sandwich the first five students buy.
 

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Student} \rule[-1ex]{0pt}{0pt} & \textbf{Sandwich Type} \\
\hline
\rule{0pt}{2.5ex} \text{Tim} \rule[-1ex]{0pt}{0pt} & \text{chicken} \\
\hline
\rule{0pt}{2.5ex} \text{Kate} \rule[-1ex]{0pt}{0pt} & \text{vegemite} \\
\hline
\rule{0pt}{2.5ex} \text{Choon} \rule[-1ex]{0pt}{0pt} & \text{vegemite} \\
\hline
\rule{0pt}{2.5ex} \text{Raj} \rule[-1ex]{0pt}{0pt} & \text{chicken} \\
\hline
\rule{0pt}{2.5ex} \text{Kelly} \rule[-1ex]{0pt}{0pt} & \text{vegemite} \\
\hline
\end{array}

 
Dom is next in line and asks for a sandwich but doesn't care which type.

What is the chance that Dom is given chicken sandwich? Give your answer as a percentage.  (2 marks)

Show Answers Only

\(60\%\)

Show Worked Solution

\(P\text{(chicken sandwich for Dom)}\)

\(=\dfrac{\text{chicken sandwiches left}}{\text{total sandwiches left}}\)

\(=\dfrac{14-2}{20}\)

\(= 0.60\)

\(= 60\%\)

Probability, SM-Bank 036 MC

A spinner can land in any of 4 sections, labelled 1 to 4.

The spinner is spun 100 times and the results are recorded in the bar chart below.
   

 

Which of these spinners is most likely to give results shown in the graph?

A. B. C. D.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Landing on 1 should be about 23% (slightly less than one quarter).}\)

\(\text{Landing on 4 should be about 52% (just over half).}\)

\(\text{Landing on 2 and 3 (combined) should be 25%.}\)
 

\(\Rightarrow D\)

Probability, SM-Bank 035

There are 50 coloured jelly beans in a bag. Twenty four jelly beans are green, the others are yellow.

Wayne picks a jelly bean from the bag without looking.

What is the chance of Wayne picking a green jelly bean?  (1 mark)

Show Answers Only

\(\dfrac{12}{25}\)

Show Worked Solution
\(P\text{(Green)}\) \(=\dfrac{24}{50}\)
  \(=\dfrac{12}{25}\)

Probability, SM-Bank 034

Francine has a bag of marbles.

The number of marbles of each colour is recorded in the table below.
 

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Colour} \rule[-1ex]{0pt}{0pt} & \textbf{Number of marbles} \\
\hline
\rule{0pt}{2.5ex} \textbf{green} \rule[-1ex]{0pt}{0pt} & 14 \\
\hline
\rule{0pt}{2.5ex} \textbf{blue} \rule[-1ex]{0pt}{0pt} & 7 \\
\hline
\rule{0pt}{2.5ex} \textbf{white} \rule[-1ex]{0pt}{0pt} & 3 \\
\hline
\rule{0pt}{2.5ex} \textbf{red} \rule[-1ex]{0pt}{0pt} & 4 \\
\hline
\end{array}  

Francine randomly takes 1 marble out of her bag without looking.

  1. What is the chance it is green?  (1 mark)
  2. What is the chance it is red or white?  (1 mark)
  3. What is the chance it is yellow?  (1 mark)
Show Answers Only

a.    \(\dfrac{1}{2}\)

b.    \(\dfrac{1}{4}\)

c.    \(0\)

Show Worked Solution
a.    \(P\text{(green)}\) \(=\dfrac{\text{Number of green}}{\text{Total number}}\)
  \(=\dfrac{14}{28}\)
  \(=\dfrac{1}{2}\)

 

b.    \(P\text{(red or white)}\) \(=\dfrac{\text{Number of red and white}}{\text{Total number}}\)
  \(=\dfrac{4+3}{28}\)
  \(=\dfrac{1}{4}\)

 
c.    \(\text{There are no yellow marbles}\)

\(\therefore\ P\text{(yellow)}=0\)

Probability, SM-Bank 033 MC

Which spinner does not show a 50-50 chance of landing on the `Delta` symbol?
 

Show Answers Only

\(A\)

Show Worked Solution

\(\text{Each of the triangle sections in the above image}\)

\(\text{only account for}\ \dfrac{1}{6}\ \text{of the pie.}\)

\(\therefore\ \text{The spinner only has}\ \dfrac{1}{3}\ \text{chance of landing}\)

\(\text{on a triangle.}\)

\(\Rightarrow A\)

Probability, SM-Bank 032

Bellamy creates a game with the spinner shown below.
 

 
If the spinner lands on a 3, he wins a prize.

What is the probability that Bellamy will win a prize on his next spin?  (1 mark)

Show Answers Only

\(\dfrac{1}{4}\)

Show Worked Solution
\(P\text{(landing on a 3)}\) \(=\dfrac{\text{Number of 3’s}}{\text{Total possibilities}}\)
  \(=\dfrac{2}{8}\)
  \(=\dfrac{1}{4}\)

Probability, SM-Bank 031

A car dealership contains 12 black, 8 red, 10 blue, 16 silver and 4 white cars.

Walter wears a blindfold and chooses one car at random.

What is the chance that the car is blue?  (2 marks)

Show Answers Only

\(\dfrac{1}{5}\)

Show Worked Solution
\(P\text{(Blue car)}\) \(=\dfrac{\text{number of blue cars}}{\text{total number of cars}}\)
  \(=\dfrac{10}{50}\)
  \(=\dfrac{1}{5}\)

Probability, SM-Bank 030

Luigi spins these two arrows. He then adds the numbers in the sections where the  arrows stop to get the total score.
 

 
How many different ways can Luigi get a total of 7?  (2 marks)

Show Answers Only

\(3\)

Show Worked Solution

\(\text{Consider the possibile ways to get 7}\)
 

 
 

\(\therefore\ \text{There are 3 ways to get a total of 7.}\)

Probability, SM-Bank 029 MC

Spiro spins the arrow of this spinner 40 times.

He records the number of times the arrow lands on each number.
 


 

Which table records the most likely results?

A.
B.
C.
D.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Landing on 1 or 5 is approximately one-third chance}\)

\(\text{which is approximately 13 times.}\)

\(\text{Landing on 4 is expected to occur slightly less often}\)

\(\text{than landing on 2 or 3.}\)

 \(\Rightarrow D\)

Probability, SM-Bank 028

Peter has a marble bag that contains 20 marbles that are either red or green in colour.

The probability of randomly picking a green marble is 70%.

  1. What is the probability of randomly picking a red marble?  (1 mark)
  2. How many red marbles are in the bag?  (1 mark)
Show Answers Only

a.    \(30\%\)

b.    \(6\)

Show Worked Solution
a.    \(P\text{(green)} + P\text{(red)}\) \(=100\%\)
\(70\% + P\text{(red)}\) \(=100\%\)
\(\therefore\ P\text{(red)}\) \(=30\%\)

 

b.    \(\text{Red marbles}\) \(=20\times 30\%\)
  \(=20\times \dfrac{3}{10}\)
  \(=6\)

Probability, SM-Bank 027 MC

Ryan has white and black marbles in his bag.

If he chooses a marble from the bag without looking he is likely, but not certain, to get a white marble.

Which is Ryan's bag?
 

A. B. C. D.

​

Show Answers Only

\(A\)

Show Worked Solution

\(\text{The 1st option gives a}\ \dfrac{3}{5}\ \text{chance of a}\)

\(\text{white marble (likely but not certain).}\)
 

\(\Rightarrow A\)

Probability, SM-Bank 026

Shirley uses this net to make a dice.

She rolls the dice once.

What is the chance that Shirley will roll a 2?  Give your answer in simplest fraction form.  (2 marks)

Show Answers Only

\(\dfrac{1}{3}\)

Show Worked Solution
\(P(2)\) \(=\dfrac{\text{Number of 2’s}}{\text{Total possibilities}}\)
  \(=\dfrac{2}{6}\)
  \(=\dfrac{1}{3}\)

Probability, SM-Bank 025 MC

Shane rolls a standard 6-sided dice once.

Which of the following is Shane most likely to roll?

  1. a number less than 3
  2. a number greater than 2
  3. an even number
  4. the number 3 or 4
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Consider the probability of each option:}\)

\(P\text{(a number less than 3)} =\dfrac{2}{6}\)

\(P\text{(a number greater than 2)} =\dfrac{4}{6}\)

\(P\text{(an even number)} =\dfrac{3}{6}=\dfrac{1}{2}\)

\(P\text{(3 or 4)} =\dfrac{2}{6}\)
 

\(\therefore\ \text{A number greater than 2 is most likely.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 023

Claudia gets to ring the school bell once every 5 school days.

Today is a school day.

What is the probability that Claudia will ring the school bell?

Show Answers Only

\(\dfrac{1}{5}\)

Show Worked Solution
\(P\text{(Claudia rings bell)}\) \(=\dfrac{\text{favorable events}}{\text{total possible events}}\)
  \(=\dfrac{1}{5}\)

Probability, SM-Bank 022

Bonny draws the number 1 or 2 on a group of discs, as pictured below.
 

 

 
One disc is chosen at random.

What is the chance the disc has a 2 drawn on it?  (1 mark)

Show Answers Only

\(\dfrac{5}{18}\)

Show Worked Solution
\(P\text{(2)}\) \(=\dfrac{\text{Number of 2’s}}{\text{Total discs}}\)
  \(=\dfrac{5}{18}\)

Probability, SM-Bank 021 MC

There are 20 raffle tickets, numbered 1 to 20, in a box.

Three prizes are given away by choosing three tickets from the box. Each ticket can win only one prize.

The first ticket drawn is number 15 and it wins the third prize.

Which of the following is not possible?
 

  1. Second prize is won by number 2.
  2. First prize is won by a prime number.
  3. Second prize is an even number.
  4. First prize is won by number 15.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{“First prize is won by number 15” is impossible because}\)

\(\text{number 15 has already been chosen and won 3rd prize.}\)

\(\text{(Note that there is no replacement of tickets.)}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 020

Jenny and Sam play a board game with the spinner shown.
 

 Jenny spins the arrow.

  1. On which number is the arrow most likely to stop?  (1 mark)
  2. What is the probability that Jenny spins a 3?  (1 mark)
  3. What is the probability that Jenny does NOT spin a 3?  (1 mark)
Show Answers Only

a.    \(3\)

b.    \(\dfrac{4}{9}\)

c.    \(\dfrac{5}{9}\)

Show Worked Solution

a.    \(\text{There are more 3’s than any other number.}\)

\(\therefore\ \text{Most likely to land on 3.}\)

b.    \(P\text{(3)}\) \(=\dfrac{\text{Number of 3’s}}{\text{Total divisions on spinner}}\)
    \(=\dfrac{4}{9}\)

 

c.    \(P\text{(not 3)}\) \(=1-P\text{(3)}\)
    \(=1-\dfrac{4}{9}\)
    \(=\dfrac{5}{9}\)

Probability, SM-Bank 019 MC

A spinner is spun once.
 

 

 
Each shape on the wheel has an equal chance.

What is the chance that the spinner lands on the triangle .
 

  1. 5 chances in 6
  2. 6 chances in 6
  3. 1 chance in 5
  4. 1 chance in 6
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Since all shapes have an equal chance,}\)

\(P\text{(triangle)}=\dfrac{1}{6}\)
 

\(\Rightarrow D\)

Probability, SM-Bank 018 MC

Kip spins the arrow on two identical spinners.

The arrow on each spinner is equally likely to land on 1, 2 or 3.
 

 
If Kip adds up the two results, which total is he least likely to get?

  1. 3
  2. 4
  3. 5
  4. 6
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Possible combinations:}\)

\((1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)\)

\(\text{A total of 6 only occurs once, (3 , 3) }\)

\(\text{so is the less likely to occur than 3, 4 or 5.}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 017 MC

Dennis is a fast bowler. In a cricket game, the chance of him getting a wicket on a given ball is unlikely.

Which probability best describes Dennis' chance of getting a wicket from one particular ball?
 

  1. \(\dfrac{14}{15}\)
  2. \(\dfrac{1}{2}\)
  3. \(1\)
  4. \(\dfrac{1}{15}\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Unlikely means the probability is}\)

\(\text{close to zero.}\)

\(\therefore\ \dfrac{1}{15}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 016 MC

The Rural Fire Service issued a statement that the chance of bushfires on a given day was extremely likely.

Which probability below best describes the chance of bushfires?

  1. \(\dfrac{1}{9}\)
  2. \(\dfrac{8}{9}\)
  3. \(1\)
  4. \(\dfrac{9}{8}\)
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Probability of  “extremely likely” is close to 1}\)

\(\text{(probability cannot > 1)}\)

\(\therefore\ \dfrac{8}{9}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 015 MC

In a high school, all the boys were asked their favourite sport and the top five results were put in the table below.

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Sport} \rule[-1ex]{0pt}{0pt} & \textbf{Number of boys} \\
\hline
\rule{0pt}{2.5ex} \text{Rugby League} \rule[-1ex]{0pt}{0pt} & \text{123} \\
\hline
\rule{0pt}{2.5ex} \text{Soccer} \rule[-1ex]{0pt}{0pt} & \text{117} \\
\hline
\rule{0pt}{2.5ex} \text{Rugby Union} \rule[-1ex]{0pt}{0pt} & \text{108} \\
\hline
\rule{0pt}{2.5ex} \text{Swimming} \rule[-1ex]{0pt}{0pt} & \text{106} \\
\hline
\rule{0pt}{2.5ex} \text{AFL} \rule[-1ex]{0pt}{0pt} & \text{100} \\
\hline
\end{array}

Which of these statements is true of a boy who goes to the high school?

  1. His favourite sport is less likely to be soccer than AFL.
  2. His favourite sport is certain to be rugby league.
  3. His favourite sport is more likely to be rugby union than swimming.
  4. It is impossible that his favourite sport is golf.
Show Answers Only

\(C\)

Show Worked Solution

\(\text{“His favourite sport is more likely to be rugby union}\)

\(\text{than swimming” is the correct statement.}\)
 

\(\Rightarrow C\)

Probability, SM-Bank 014 MC

The weather report says there is 80% chance of rain tomorrow.

Which of these describes the chance of it raining tomorrow?

  1. impossible
  2. unlikely
  3. likely
  4. certain
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Anything over 50% chance has more likelihood of}\)

\(\text{happening than not. Anything that is certain to}\)

\(\text{happen must be 100% chance.}\)

\(\therefore\ \text{80% chance is “likely”.}\)

 
\(\Rightarrow C\)

Probability, SM-Bank 013 MC

Mick has a bag of marbles. His marbles are orange, white, blue and green.
 

 
Mick picks one marble from his bag.

Which of the following could be the probability that the marble he picks is green.

  1. \(\dfrac{13}{3}\)
  2. \(1.52\)
  3. \(\dfrac{3}{13}\)
  4. \(6\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Any probability must be between 0 and 1 inclusive.}\)

\(\therefore\ \text{Only possibility is }\dfrac{3}{13}\)

 
\(\Rightarrow C\)

Probability, SM-Bank 012 MC

Two identical spinners are spun at the same time and the two numbers they land on are added up.
 

 
Which total is most likely?

  1. 4
  2. 7
  3. 10
  4. 12
Show Answers Only

\(B\)

Show Worked Solution

\(\text{A total of 7 can be achieved in 6 different ways.}\)

\(\text{All other totals have less possible combinations.}\)

\(\therefore\ \text{a total of 7 is the most likely.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 011 MC

A small disc is thrown onto the grid pictured below.
 

The disc has an equal chance of landing in any square.

Which numbered square is the disc least likely to land in?

  1. 3
  2. 4
  3. 5
  4. All numbers are equally likely
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Only 1 square is numbered 4 (all other numbers}\)

\(\text{have 2 squares).}\)

\(\therefore\ \text{The disc is least likely to land on the number 4.}\)

   
\(\Rightarrow B\)

Probability, SM-Bank 010 MC

A spinning wheel has sections labelled with different numbers.
 
 

If the spinner has an equal chance of landing in each section, which of the numbers is the spinner most likely to land on?

  1. 1 or 3
  2. 1
  3. 2 or 4
  4. All of the numbers are equally likely
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Since the spinner is divided into 8 equal sections}\)

\(\text{and each number has 2 sections, all numbers}\)

\(\text{are equally likely.}\)

   
\(\Rightarrow D\)

Probability, SM-Bank 009 MC

The arrow pictured below is spun once: 

Which number is the spinner most likely to land on?

  1. 1
  2. 2
  3. 3
  4. Same chance for each number.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{The sections that are labelled with a 2 are}\)

\(\text{the largest when combined.}\)

\(\therefore\ \text{Spinner most likely to land on 2.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 008 MC

A standard deck of 52 cards is made up of four suits - Hearts, Diamonds, Clubs and Spades.

Each suit contains 13 cards that include an Ace, King, Queen and Jack, together with numbered cards from 2 to 10.

Lara has a standard deck of cards and without looking, picks a number 7 and returns it to the deck.

She repeats this three times and draws a number 7 each time.

If she draws a 4th card without looking, which of the following is true?
 

  1. She is certain to draw a number 7.
  2. She is more likely to draw a number 7 than a Spade.
  3. She is less likely to draw a number 7 than a Queen.
  4. She is more likely to draw a Heart than a number 7.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{There are 13 hearts in the deck}\)

\(\text{There are 13 spades in the deck}\)

\(\text{There are 4 7’s in the deck}\)

\(\text{There are 4 queens in the deck}\)
 

\(\text{Consider Option D}\ \rightarrow\ \text{There are more hearts than 7’s}\)

\(\therefore\ \text{She is more likely to draw a heart than a 7}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 007 MC

Eight buttons, numbered 1 to 8, are placed in a bag.

Robin picks three buttons out of the bag without looking.

Once chosen, a button is not put back into the bag.

The first button is number 2.

Which of the following cannot happen?

  1. The second button is even.
  2. The third button is 2.
  3. The second button is odd.
  4. The third button is 8.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{Once number 2 is picked, it cannot be}\)

\(\text{picked again (no replacement).}\)

\(\therefore\ \text{The third button cannot be 2.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 006 MC

Shapes are drawn on the balls below and placed in a bag.
 

 

Billy reaches into the bag and takes out a ball without looking.

Which type of ball is he least likely to take out?

A.
B.
C.
D.
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Counting the balls of each type:}\)

\(6\times\)
\(5\times\)
\(3\times\)
\(2\times\)

 

\(\therefore\ \text{Least likely is  }\)

\(\Rightarrow A\)

Probability, SM-Bank 005 MC

These identical numbered discs were in a bag.

Julio selected one disc.
 

 

What is the chance that the disc Julio selected had a number less than 10 on it?

  1. Unlikely
  2. Certain
  3. Impossible
  4. Even
Show Answers Only

\(B\)

Show Worked Solution

\(\text{All the discs have numbers less than ten.}\)

\(\text{Therefore, the chance of a number being selected

\(\text{that is less than 10 is certain.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 004 MC

Which of the following spinners is the least likely to land on the coloured area?
A. B.

C. D.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{This spinner has the least area painted therefore}\)

\(\text{has the least chance of landing on a coloured}\)

\(\text{portion of the spinner.}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 003 MC

Which of the following spinners will most likely land on the coloured area?
A. B.

C. D.
Show Answers Only

\(B\)

Show Worked Solution

\(\text{This spinner has the most area painted therefore}\)

\(\text{has the highest chance of landing on a coloured}\)

\(\text{portion of the spinner.}\)

 
\(\Rightarrow B\)

Probability, SM-Bank 002 MC

A statistic shows that on a certain highway the chance of an accident happening on any day is 5%.

Which of the following describes the chance of having an accident today?

  1. Likely
  2. Certain
  3. Impossible
  4. Unlikely
Show Answers Only

\(D\)

Show Worked Solution

\(\text{An event with 100% chance of occurring is certain to happen.}\)

\(\text{The chance of an accident happening today is 5%.}\)

\(\therefore\ \text{It is unlikely to happen since the chance is very low.}\)

 
\(\Rightarrow D\)

Probability, SM-Bank 001 MC

These identical numbered discs were in a bag.

Gay selected one disc.
 


 

What is the chance that the disc Gay selected had a 7 on it?

  1. Unlikely
  2. Certain
  3. Impossible
  4. Even
Show Answers Only

\(C\)

Show Worked Solution

\(\text{The discs have the following numbers:}\)

\(\text{There are no discs with a 7}\)

\(\therefore\ \text{The chance the selected disc has a 7 on it is impossible.}\)

 
\(\Rightarrow C\)

Interpreting Data, SM-Bank 031

Judge recorded 2 hourly temperatures from the Bureau of Meteorology for his home town, for a 24 hour period beginning at midnight.

  1. What was the temperature at 2 a.m.?  (1 mark)
  2. At what time was the minimum temperature for the 24 hour period?  (1 mark)
  3. What was the range of temperatures?  (1 mark)
  4. Use the graph to estimate the 2 times of the day when the temperature was 18°C?  (1 mark)

  5. Use the graph to estimate the temperature at:
    i.    7:00 a.m.  (1 mark)

    ii.   9:30 a.m.  (1 mark)

    iii.  5:00 p.m.  (1 mark)

Show Answers Only

a.    \(13 ^{\circ }\text{C}\)

b.    \(6:00\ \text{a.m.}\)

c.    \(16^{\circ }\text{C}\)

d.    \(9:00\ \text{a.m. and }9:30\ \text{p.m.}\)

e.    i.    \(12 ^{\circ }\text{C}\)

ii.   \(20 ^{\circ }\text{C}\)

iii.  \(25 ^{\circ }\text{C}\)

Show Worked Solution

a.    \(13 ^{\circ }\text{C}\)

b.    \(6:00\ \text{a.m.}\)

c.    \(16^{\circ }\text{C}\)

d.    \(9:00\ \text{a.m. and }9:30\ \text{p.m.}\)

e.    i.    \(12 ^{\circ }\text{C}\)

ii.   \(20 ^{\circ }\text{C}\)

iii.  \(25 ^{\circ }\text{C}\)