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Probability, SM-Bank 085

Jordan and Degas play a board game with the spinner shown.
 

 
Jordan spins the arrow.

  1. What is the probability that Jordan spins an even number?  (1 mark)
  2. To win the game you must spin an odd number.
    What is the probability that Jordan will win the game on the next spin?  (1 mark)

Show Answers Only

a.    \(\dfrac{1}{3}\)

b.    \(\dfrac{2}{3}\)

Show Worked Solution
a.    \(P\text{(Even)}\) \(=\dfrac{\text{# even numbers}}{\text{Total numbers}}\)
    \(=\dfrac{3}{9}\)
    \(=\dfrac{1}{3}\)

 

b.    \(P\text{(Odd)}\) \(=1-P\text{(Even)}\)
    \(=1-\dfrac{1}{3}\)
    \(=\dfrac{2}{3}\)

Probability, SM-Bank 069

Wendy has a number of different types of flowers as shown in the table below. 
 

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textbf{Type of Flower} \rule[-1ex]{0pt}{0pt} & \textbf{Number of Flowers} \\
\hline
\rule{0pt}{2.5ex} \text{Carnation} \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\rule{0pt}{2.5ex} \text{Tulip} \rule[-1ex]{0pt}{0pt} & 6 \\
\hline
\rule{0pt}{2.5ex} \text{Dandelion} \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Rose} \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\end{array}

  1. What is the probability that a randomly selected flower will be either a carnation or a tulip?  (2 marks)
  2. What is the probability that a randomly selected flower will not be a rose?  (2 marks)

Show Answers Only

a.    \(\dfrac{7}{16}\)

b.    \(\dfrac{3}{4}\)

Show Worked Solution
a.    \(P\text{(carnation or tulip)}\) \(=\dfrac{\text{number carnations + number tulips}}{\text{total number of flowers}}\)
    \(=\dfrac{8+6}{32}\)
    \(=\dfrac{14}{32}=\dfrac{7}{16}\)

 

b.    \(P\text{(not a rose)}\) \(=1-P\text{(is a rose)}\)
    \(=1-\dfrac{\text{number roses}}{\text{total number of flowers}}\)
    \(=1-\dfrac{8}{32}\)
    \(=1-\dfrac{1}{4}\)
    \(=\dfrac{3}{4}\)

Probability, SM-Bank 067

A bag of coloured balls contains 10 blue balls, 12 white balls, 5 black balls, 2 red balls, and 9 orange balls.

Joyce grabs a ball from the bag without looking what is inside.

What is the probability that she grabs an white ball?  (1 mark)

Show Answers Only

\(\dfrac{6}{19}\)

Show Worked Solution
\(P\text{(White ball)}\) \(=\dfrac{\text{Total white balls}}{\text{Total balls}}\)
  \(=\dfrac{12}{10+12+5+2+9}\)
  \(=\dfrac{12}{38}\)
  \(=\dfrac{6}{19}\)

Probability, SM-Bank 066

A bag contains different coloured balls.

It contains 4 red balls, 8 green balls, 3 pink balls, 6 grey balls and 11 yellow balls.

Nathalie picks a ball from the bag without looking.

  1. What is the chance that she draws a grey ball?  (1 mark)
  2. What is the chance that the ball she draws in not pink?  (2 marks)

Show Answers Only

a.    \(\dfrac{3}{16}\)

b.    \(\dfrac{29}{32}\)

Show Worked Solution
a.    \(P\text{(Grey ball)}\) \(=\dfrac{\text{Number of grey balls}}{\text{Total number of balls}}\)
    \(=\dfrac{6}{4+8+3+6+11}\)
    \(=\dfrac{6}{32}\)
    \(=\dfrac{3}{16}\)

 

b.    \(P\text{(not pink ball)}\) \(=1-P\text{(pink ball)}\)
    \(=1-\dfrac{\text{Number of pink balls}}{\text{Total number of balls}}\)
    \(=1-\dfrac{3}{32}\)
    \(=\dfrac{29}{32}\)

Probability, SM-Bank 063

Victoria runs a pet store that sells pure breed dogs.

She has several dogs in the shop from different breeds.
 


 

  1. If one of Victoria's dogs is chosen at random, what is the probability it will be either a labrador or a pug?  (1 mark)

  2. If one of the dogs is chosen at random, what is the probability that the dog is not a bulldog?  (2 marks)
Show Answers Only

a.    \(\dfrac{5}{9}\)

b.    \(\dfrac{5}{6}\)

Show Worked Solution
a.    \(P\text{(Labrador or Pug)}\) \(=\dfrac{\text{Number of Labrador and Pug}}{\text{Total dogs}}\)
    \(=\dfrac{16 + 4}{4+16+6+5+5}\)
    \(=\dfrac{20}{36}=\dfrac{5}{9}\)

 

b.    \(P\text{(Dog not a bulldog)}\) \(=1-P\text{(Dog is a bulldog)}\)
    \(=1-\dfrac{6}{36}\)
    \(=\dfrac{30}{36}=\dfrac{5}{6}\)

Probability, SM-Bank 061

Chusi uses this net to make a dice.
 

  
  1. Chusi rolls the dice once. What is the chance that Chusi will roll a 2? (1 mark)
  2. Chusi makes up a game and to win the game you must roll a number larger than 2.
    What is the chance that Chusi will win the game on her next roll?  (1 mark)

  3. If Chusi rolls the dice 108 times, how many times could she expect to win the game?  (1 mark)
Show Answers Only

a.    \(\dfrac{1}{3}\)

b.    \(\dfrac{1}{6}\)

c.    \(18\ \text{times}\)

Show Worked Solution
a.    \(P(2)\) \(=\dfrac{\text{number of 2’s}}{\text{total possibilities}}\)
    \(=\dfrac{2}{6}\)
    \(=\dfrac{1}{3}\)

 

b.    \(P\text{(number>2)}\) \(=\dfrac{\text{number of 3’s}}{\text{total possibilities}}\)
    \(=\dfrac{1}{6}\)

\(\therefore\ \text{Chusi’s chance of winning on the next roll is }\dfrac{1}{6}.\)
 

c.    \(\text{Expected wins}\) \(=\text{number of rolls}\times \text{probability of winning}\)
    \(=108\times \dfrac{1}{6}\)
    \(=18\)

\(\therefore\ \text{Chusi could expect to win 18 times with 108 rolls.}\)

Probability, SM-Bank 060 MC

Benji randomly picks one disc from the group of white and coloured discs, pictured below.
 

 

 
What is the probability Benji chooses a white disc?

  1. \(\dfrac{2}{3}\)
  2. \(\dfrac{8}{13}\)
  3. \(\dfrac{8}{21}\)
  4. \(\dfrac{13}{21}\)
Show Answers Only

\(D\)

Show Worked Solution
\(P\text{(White disc)}\) \(=\dfrac{\text{Number of white discs}}{\text{Total discs}}\)
  \(=\dfrac{13}{21}\)

\(\Rightarrow D\)

Probability, SM-Bank 059 MC

Ashanti works in the city on weekdays and has weekends off.

She catches a bus to work 3 days each week and drives two days.

If today is a weekday, what is the probability that Ashanti catches a bus to work?

  1. \(3\%\)
  2. \(0.30\)
  3. \(\dfrac{3}{7}\)
  4. \(\dfrac{3}{5}\)
Show Answers Only

\(D\)

Show Worked Solution
\(P\text{(Bus)}\) \(=\dfrac{\text{favourable events}}{\text{total possible events}}\)
  \(=\dfrac{3}{5}\)

\(\Rightarrow D\)

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 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 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 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 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 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 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 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 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, STD1 S2 2023 HSC 8 MC

Four cards marked with the numbers 1, 2, 3 and 4 are placed face down on a table.

One card is turned over as shown.

What is the probability that the next card turned over is marked with an odd number?

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

\(D\)

Show Worked Solution

\(\text{Sample space} =1,3,4\)

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

  
\(\Rightarrow D\)

Probability, STD1 S2 2022 HSC 17

Each number from 1 to 30 is written on a separate card. The 30 cards are shuffled. A game is played where one of these cards is selected at random. Each card is equally likely to be selected.

Ezra is playing the game, and wins if the card selected shows an odd number between 20 and 30.

  1. List the numbers which would result in Ezra winning the game.  (1 mark)

  2. What is the probability that Ezra does NOT win the game?  (2 marks)

Show Answers Only
  1. `21, 23, 25, 27, 29`
  2. `Ptext{(not win)} = 5/6`
Show Worked Solution

a.   `21, 23, 25, 27, 29`
 

b.    `Ptext{(not win)}` `=1-Ptext{(win)}`
    `=1-5/30`
    `=25/30`
    `=5/6`


♦ Mean mark 51%.

Probability, STD1 S2 2021 HSC 20

In a bag, there are six playing cards, 2, 4, 6, 8, Queen and King. The Queen and King are known as picture cards.

Two of these cards are chosen randomly. All the possible outcomes are shown.
 

   
 

  1. What is the probability that the two cards chosen include one or both picture cards?  (1 mark)

  2. What is the probability that the two cards chosen do NOT include any picture cards?  (1 mark)

Show Answers Only
  1. `9/15`
  2. `6/15`
Show Worked Solution

a.   `P text{(at least 1 picture card)} = 9/15`

 

b.    `P text{(no picture card)}` `= 1 – 9/15`
    `= 6/15`

Probability, STD2 S2 2017 HSC 15 MC

The faces on a twenty-sided die are labelled  $0.05, $0.10, $0.15, … , $1.00.

The die is rolled once.

What is the probability that the amount showing on the upper face is more than 50 cents but less than 80 cents?

A.     `1/4`

B.     `3/10`

C.     `7/20`

D.     `1/2`

Show Answers Only

`A`

Show Worked Solution

`text(Possible faces that satisfy are:)`

♦ Mean mark 50%.

`55text(c),60text(c),65text(c),70text(c),75text(c)`

`:.\ text(Probability)` `= 5/20`
  `= 1/4`

`=>A`

Probability, STD2 S2 2005 HSC 11 MC

The diagram shows a spinner.
 


 

The arrow is spun and will stop in one of the six sections.

What is the probability that the arrow will stop in a section containing a number greater
than 4?

  1.    `2/5`
  2.    `2/3`
  3.    `1/3`
  4.    `1/2`
Show Answers Only

`D`

Show Worked Solution

`P\ text((number greater than 4))`

`= P(7) + P (9)`

`= 2/6 + 1/6`

`= 1/2`

`=>  D`

Probability, STD2 S2 2008 HSC 16 MC

A bag contains some marbles. The probability of selecting a blue marble at random from this bag is  `3/8`.

Which of the following could describe the marbles that are in the bag?

  1.    `3`  blue,  `8`  red
  2.    `6`  blue,  `11`  red
  3.    `3`  blue,  `4`  red,  `4`  green
  4.    `6`  blue,  `5`  red,  `5`  green 
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`D`

Show Worked Solution

`P(B) = 3/8`

`text(In)\ A,\ \ ` `P(B) = 3/11`
`text(In)\ B,\ \ ` `P(B) = 6/17 `
`text(In)\ C,\ \ ` `P(B) = 3/11`
`text(In)\ D,\ \ ` `P(B) = 6/16 = 3/8`

`=>  D`

Probability, STD2 S2 2010 HSC 23c

On Saturday, Jonty recorded the colour of T-shirts worn by the people at his gym. The results are shown in the graph.

 

  1. How many people were at the gym on Saturday? (Assume everyone was wearing a T-shirt).   (1 mark)

  2. What is the probability that a person selected at random at the gym on Saturday, would be wearing either a blue or green T-shirt?   (1 mark)

Show Answers Only
  1. `34`
  2. `15/34`
Show Worked Solution
i.   `text(# People)` `=5+15+10+3+1`
  `=34`

 

ii.   `P (B\ text{or}\ G)` `=P(B)+P(G)`
  `=5/34+10/34`
  `=15/34`

Probability, STD2 S2 2010 HSC 8 MC

A bag contains red, green, yellow and blue balls.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Colour} \rule[-1ex]{0pt}{0pt} & \textit{Probability} \\
\hline
\rule{0pt}{2.5ex} \text{Red} & \dfrac{1}{3} \\
\hline
\rule{0pt}{2.5ex} \text{Green}  & \dfrac{1}{4} \\
\hline
\rule{0pt}{2.5ex} \text{Yellow}  & \text{?} \\
\hline
\rule{0pt}{2.5ex} \text{Blue}  & \dfrac{1}{6} \\
\hline
\end{array}

The table shows the probability of choosing a red, green, or blue ball from the bag.

If there are 12 yellow balls in the bag, how many balls are in the bag altogether

  1.    16
  2.    36
  3.    48
  4.    60
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\(C\)

Show Worked Solution
\(P(R)+P(G)+P(Y)+P(B)\) \(=1\)
\(\dfrac{1}{3}+\dfrac{1}{4}+P(Y)+\dfrac{1}{6}\) \(=1\)
\(P(Y)\) \(= 1-(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{6})\)
  \(=1-\dfrac{9}{12}\)
  \(=\dfrac{1}{4}\)
\(P(Y)\) \(=\dfrac{\text{Yellow balls}}{\text{Total balls}}\)
\(\dfrac{1}{4}\) \(=\dfrac{12}{\text{Total balls}}\)

 

\(\therefore\ \text{ Total balls}=48\)

\(\Rightarrow C\)

Probability, STD2 S2 2013 HSC 1 MC

Which of the following events would be LEAST likely to occur?

  1.    Tossing a fair coin and obtaining a head
  2.    Rolling a standard six-sided die and obtaining a 3
  3.    Randomly selecting the letter 'G' from the 26 letters of the alphabet
  4.    Winning first prize in a raffle of 100 tickets in which you have 4 tickets
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`C`

Show Worked Solution

`P(A)=1/2,\ \ P(B)=1/6`

`P(C)=1/26,\ \ P(D)=4/100=1/25`

 

`=>C\ text(is the least likely.)`