ProbabilityFoundation and Higher

Probability GCSE questions with answers

8 probability questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

Probability questions cover single events, the chance that something does not happen, missing values in a table, expected results and relative frequency. You also find probabilities for two events, including two picks without replacement and two dice.

Quiz yourself: 8 questions

Worked example 1: probability of one event

A bag has 3 yellow and 6 green beads. One is taken at random. Work out the probability that it is green.

There are 3 + 6 = 9 beads altogether.
6 of them are green.
Probability = 6 out of 9 = 69, which simplifies to 23.

Answer 23

01 / Quiz yourselfTry it, then tap to check

Probability questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Probability of one eventBoth tiers

A bag has 8 white and 3 red counters. One is taken at random. Work out the probability that it is red.

Show the answer and working

There are 8 + 3 = 11 counters altogether.
3 of them are red.
Probability = 3 out of 11 = 311.

Answer 311

02 / The probability something does not happenBoth tiers

The probability that it will rain tomorrow is 35. Work out the probability that it will not rain tomorrow.

Show the answer and working

Something either happens or it does not, so the two probabilities add up to 1.
1 − 35 = 25.

Answer 25

03 / Missing probabilities in a tableBoth tiers

A biased spinner can land on 1, 2, 3 or 4. The table shows the probability of each number. Work out the probability that it lands on 4.

Show the answer and working

All the probabilities add up to 1. The ones you know add up to 0.19 + 0.27 + 0.36 = 0.82.
1 − 0.82 = 0.18.

Answer 0.18

04 / Expected resultsBoth tiers

The probability that a player scores from a penalty is 0.7. The player takes 40 penalties. How many goals would you expect?

Show the answer and working

Expected number = probability × number of tries.
0.7 × 40 = 28.

Answer 28

05 / Relative frequencyBoth tiers

A dice is rolled 100 times. The table shows the results. Work out the relative frequency of getting a 3.

Show the answer and working

Relative frequency = number of times it happened ÷ number of tries.
20 ÷ 100 = 20100 = 15.

Answer 15

06 / Two events: and, orBoth tiers

Two spinners are spun. The spinners are independent. The probability the first lands on red is 0.25. The probability the second lands on blue is 0.8. Work out the probability that the first lands on red and the second lands on blue.

Show the answer and working

The two events do not affect each other, so multiply the probabilities for "and".
P(red on the first) = 0.25, P(blue on the second) = 0.8.
0.25 × 0.8 = 0.2.

Answer 0.2

07 / Two dice: sample spaceBoth tiers

Two fair dice are rolled and the scores are added. The table shows every possible total. Work out the probability that the total is 10.

Show the answer and working

There are 6 × 6 = 36 equally likely results.
Count the totals in the table that fit: 3.
Probability = 336 = 112.

Answer 112

08 / Two picks without replacementBoth tiers

A bag has 5 black and 4 green counters. Two counters are taken at random, one after the other, without replacement (the first one is not put back). Work out the probability that both are the same colour.

Show the answer and working

Both black: 59 × 48 = 2072.
Both green: 49 × 38 = 1272.
Either way: add them, 3272 = 49.

Answer 49

02 / What's covered8 kinds of question

Probability at GCSE and where marks go

Probability of one eventBoth tiers
The probability something does not happenBoth tiers
Missing probabilities in a tableBoth tiers
Expected resultsBoth tiers
Relative frequencyBoth tiers
Two events: and, orBoth tiers
Two dice: sample spaceBoth tiers
Two picks without replacementBoth tiers

Worked example 2: two picks without replacement

A bag has 4 blue and 7 green counters. Two counters are taken at random, one after the other, without replacement (the first one is not put back). Work out the probability that both are the same colour.

Both blue: 411 × 310 = 12110.
Both green: 711 × 610 = 42110.
Either way: add them, 54110 = 2755.

Answer 2755

A common mistake

Keeping the same fraction for the second pick without replacement. From a bag of 3 red and 2 blue counters, P(two red) = 3/5 × 2/4 = 6/20 = 3/10, because one red has gone before the second pick.

03 / Practise itiPhone and iPad

Probability GCSE questions with answers

Worked example 1: probability of one event

Probability questions to try

A bag has 8 white and 3 red counters. One is taken at random. Work out the probability that it is red.

The probability that it will rain tomorrow is 35. Work out the probability that it will not rain tomorrow.

A biased spinner can land on 1, 2, 3 or 4. The table shows the probability of each number. Work out the probability that it lands on 4.

The probability that a player scores from a penalty is 0.7. The player takes 40 penalties. How many goals would you expect?

A dice is rolled 100 times. The table shows the results. Work out the relative frequency of getting a 3.

Two spinners are spun. The spinners are independent. The probability the first lands on red is 0.25. The probability the second lands on blue is 0.8. Work out the probability that the first lands on red and the second lands on blue.

Two fair dice are rolled and the scores are added. The table shows every possible total. Work out the probability that the total is 10.

A bag has 5 black and 4 green counters. Two counters are taken at random, one after the other, without replacement (the first one is not put back). Work out the probability that both are the same colour.

Probability at GCSE and where marks go

Worked example 2: two picks without replacement

A common mistake

More probability questions in Show Working

More probability topics