O Level / IGCSE Mathematics chapter 8: Probability MCQs with answers
By Team Megalecture · Updated 4 Nov 2026
27 exam-style questions on Probability, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.
Try each one, then open the answer. These ten stay the same; the test draws new ones every time.
1. The probability that a bus is late on any day is 0.2, independently of other days. Find the probability that over two days it is late on exactly one day.
A
0.16
B
0.04
C
0.32
D
0.36
Show answer
Answer: C. On a tree diagram there are two branches: late then not late (0.2 × 0.8) and not late then late (0.8 × 0.2). Total 0.16 + 0.16 = 0.32. Counting only one branch gives 0.16.
2. Four students each toss the same coin to estimate the probability of a head. Whose result gives the most reliable estimate?
A
Bina: 52 heads in 100 tosses
B
Dev: 3 heads in 5 tosses
C
Chen: 240 heads in 500 tosses
D
Ali: 9 heads in 20 tosses
Show answer
Answer: C. Relative frequency becomes a more reliable estimate as the number of trials increases, so the 500 tosses give the best estimate.
3. Two fair six-sided dice are rolled and their scores are added. Find the probability that the total is 8.
A
1/12
B
1/11
C
5/36
D
1/6
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Answer: C. Totals of 8 come from (2, 6), (3, 5), (4, 4), (5, 3) and (6, 2): 5 out of 36 equally likely outcomes. 1/11 wrongly treats the 11 totals as equally likely.
4. In a class of 30 students, 18 study French, 12 study Spanish and 5 study both. A student is chosen at random. Find the probability that they study neither language.
A
1/10
B
1/6
C
0
D
13/30
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Answer: B. In a Venn diagram: French only 13, Spanish only 7, both 5, total 25. Neither = 30 − 25 = 5, so P = 5/30 = 1/6. Doing 30 − 18 − 12 = 0 counts the 5 twice.
5. The probability that a seed grows is 0.85. If 240 seeds are planted, how many would you expect NOT to grow?
A
204
B
85
C
15
D
36
Show answer
Answer: D. P(not grow) = 1 − 0.85 = 0.15. Expected number = 0.15 × 240 = 36. 204 is the number expected to grow.
6. A biased coin has P(head) = 0.6. The expected number of heads is 48. How many times was the coin tossed?
A
80
B
60
C
120
D
28.8
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Answer: A. Expected number = probability × tosses, so 48 = 0.6 × n and n = 48 ÷ 0.6 = 80. Multiplying 48 by 0.6 gives 28.8.
7. A, B and C are the only possible outcomes of an experiment and no two can happen together. P(A) = 0.3 and P(B) = 0.45. Find P(C).
A
0.75
B
0.15
C
0.25
D
0.135
Show answer
Answer: C. The probabilities of all the outcomes add to 1: P(C) = 1 − 0.3 − 0.45 = 0.25.
8. A bag contains 3 red, 5 blue and 4 green counters. One counter is taken at random. Find the probability that it is not blue.
A
5/12
B
7/12
C
1/3
D
2/3
Show answer
Answer: B. There are 12 counters. P(blue) = 5/12, so P(not blue) = 1 − 5/12 = 7/12 (the 3 red and 4 green).
9. A biased dice is rolled 200 times and a six comes up 46 times. Estimate the probability of rolling a six with this dice.
A
0.46
B
0.23
C
1/6
D
46
Show answer
Answer: B. Relative frequency = 46/200 = 0.23. This is an estimate of the probability; 1/6 would only apply to a fair dice.
10. A fair six-sided dice is rolled twice. Find the probability of getting at least one six.
A
1/36
B
25/36
C
1/3
D
11/36
Show answer
Answer: D. P(no six) = 5/6 × 5/6 = 25/36, so P(at least one six) = 1 − 25/36 = 11/36. Adding 1/6 + 1/6 = 1/3 counts a double six twice.
27, each with the answer and a short explanation, across 3 topics: Introduction to probability, Relative and expected frequencies, Probability of combined events. Every chapter test draws ten of them, so you can take it many times.
Is the O Level / IGCSE Mathematics chapter 8 test free?
Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.
How is the chapter test marked?
The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.
