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Year 9 · Practice

Probability of Combined Events — Year 9 Practice Questions

Work through these Year 9 practice questions on the probability of combined events. Try each one before revealing the worked solution.

Questions

1
[2 marks] Easy Sample space

Two coins are flipped. List all the possible outcomes.

2
[2 marks] Medium Combined

Two coins are flipped. Find the probability of getting two heads.

3
[1 marks] Easy Sample space

How many outcomes are there when two ordinary dice are rolled?

4
[2 marks] Medium Independent

Two dice are rolled. Find the probability that both show a 6.

5
[2 marks] Medium Independent

A coin is flipped and a dice is rolled. Find the probability of a head and a 4.

6
[3 marks] Hard Sample space

Two dice are rolled. Find the probability that the total is 7.

7
[2 marks] Medium Independent with replacement

A bag has a red and a blue counter. A counter is taken, replaced, then another is taken. Find the probability of two reds.

8
[3 marks] Hard Independent

The probability a spinner lands on green is 0.4. It is spun twice. Find the probability it lands on green both times.

Answers & Worked Solutions

Question 1 Solution

Step 1: Each coin can be H or T.

Step 2: The outcomes are HH, HT, TH, TT.

Answer: HH, HT, TH, TT

Question 2 Solution

Step 1: There are 4 equally likely outcomes; only HH is two heads.

Step 2: P(two heads) = 1/4.

Answer: 1/4

Question 3 Solution

Step 1: Each dice has 6 outcomes.

Step 2: 6 × 6 = 36.

Answer: 36

Question 4 Solution

Step 1: P(6) on each dice is 1/6.

Step 2: 1/6 × 1/6 = 1/36.

Answer: 1/36

Question 5 Solution

Step 1: P(head) = 1/2 and P(4) = 1/6.

Step 2: 1/2 × 1/6 = 1/12.

Answer: 1/12

Question 6 Solution

Step 1: The pairs giving 7 are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — 6 outcomes.

Step 2: 6 out of 36 = 1/6.

Answer: 1/6

Question 7 Solution

Step 1: P(red) = 1/2 each time, and the events are independent.

Step 2: 1/2 × 1/2 = 1/4.

Answer: 1/4

Question 8 Solution

Step 1: The spins are independent, each P(green) = 0.4.

Step 2: 0.4 × 0.4 = 0.16.

Answer: 0.16

Topic Overview

Revision Notes

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