The fish in a pond are to be removed for the pond to be cleaned. There are 4 different types of coloured carp in the pond.

Calculate the probability that the first carp captured is orange, given the probability of capturing:

• a red carp is \(\dfrac{2}{9}\)
• a white carp is \(\dfrac{1}{6}\) and
• a mulit-coloured carp is \(\dfrac{5}{12}\).  (2 marks)

A spinner with equal divisions has the numbers 1, 2 and 3 printed on it.

The probability of spinning the number 2 is \(\dfrac{1}{5}\) and the probability of spinning the number 3 is \(\dfrac{2}{3}\).

What is the probability of spinning the number 1?  (2 marks)

A bag contains a number of identical red, blue and green discs.

The probability of drawing a red disc is \(\dfrac{2}{3}\) and the probability of drawing a blue disc is \(\dfrac{1}{4}\).

What is the probability of drawing a green disc?  (2 marks)

A 12 sided die is rolled. List the favourable outcomes for this event where the number rolled is less than 6.  (1 mark)

Which percentage description best describes an event that is likely to occur?

1. \(\text{Equal to }50\%\)
2. \(\text{Equal to }0\%\)
3. \(\text{Greater than }0\%\ \text{but less than }50\%\)
4. \(\text{Greater than }50\%\ \text{but less than }100\%\)

The letters from the word KITCHEN are written on cards and one is drawn at random.

1. List the elements of the sample space.  (1 mark)

   --- 1 WORK AREA LINES (style=lined) ---

2. List the favourable outcomes if the letter chosen is NOT a vowel (a,e, i, o, u).  (1 mark)

   --- 1 WORK AREA LINES (style=lined) ---

3. For the letter chosen, find \(P\)(letter is a vowel).  (1 mark)

   --- 2 WORK AREA LINES (style=lined) ---

A spinner has 8 equal divisions numbered using the even numbers from 2 to 16.

List the sample space for this spinner.  (1 mark)

Guy is going to throw a ten sided dice labelled with the numbers 1 to 10.

He is interested in the likelihood of various events.

1. List the sample space for throwing this dice.  (1 mark)

   --- 1 WORK AREA LINES (style=lined) ---

2. List the favourable outcomes if Guy wants a number greater than 7.  (1 mark)

   --- 1 WORK AREA LINES (style=lined) ---

3. List the favourable outcomes if Guy wants an odd number less than 5.  (1 mark)

   --- 1 WORK AREA LINES (style=lined) ---

4. Which of the events from (b) and (c) above is more likely?  (1 mark)

   --- 1 WORK AREA LINES (style=lined) ---

Ahmed rolled a standard 6-sided dice a number of times. He noticed after numerous rolls that the 5 and 6 were twice as likely to occur than any of the other numbers.

Use the numbers 1, 2, 3, 4, 5 and 6 on the spinner below to create a spinner that would give the same results.  (1 mark)
 

Using the numbers 1, 2 and 3 label, the spinner below so that 3 is twice as likely to occur as either of the other numbers.  (1 mark)
 

Shade the spinner below so that white is 2 times more likely to occur than grey.  (1 mark)
 

Shade the spinner below so that white is 2 times more likely to occur than grey.  (1 mark)
 

Shade the spinner below so that white is 3 times more likely to occur than grey.  (1 mark)
 

Shade the spinner below so that grey and white have an even chance of occurring.  (1 mark)
 

Given that white and yellow are equally likely, shade the spinner below so that blue is twice as likely to occur as either white or yellow.  (1 mark)
 

Shade the spinner below so that blue is certain to occur.  (1 mark)
 

Shade the spinner below so that white is 3 times more likely to occur than blue.  (1 mark)
 

Shade the spinner below so that blue and white have an even chance of occurring.  (1 mark)
 

Newton holds an apple in his outstretched hand and releases it.

Which number below represents the probability that it will travel towards the ground?

1. 0.0
2. 0.5
3. 1.0
4. 1.99

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

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.

​

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.

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

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

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

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.

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

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. \(6\)

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

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

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

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.

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.

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.

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

A.
B.
C.
D.

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

1. Likely
2. Certain
3. Impossible
4. Unlikely

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