Prepared by Mohsim Digital Education

Probability Practice Problems with Solutions - IGCSE Year 11

IGCSE Year 11 | Math | Probability
Name: _________________________ Date: _________________________ Score: _______ / 40

Rolling a fair die gives a 1 ÷ 6 chance of a 3, and two heads from two coins comes out at 1 ÷ 4, so this Year 11 sheet opens with single-outcome and paired-outcome probabilities. The answers add 0 for an impossible event and 2 ÷ 5 for a coloured ball.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. A fair die is rolled once. What is the probability of scoring a 3?
(a) 1 ÷ 2(b) 1 ÷ 3(c) 1 ÷ 6(d) 1 ÷ 4
2. A fair coin is tossed twice. What is the probability of getting two heads?
(a) 1 ÷ 2(b) 1 ÷ 4(c) 1 ÷ 3(d) 1 ÷ 8
3. What is the probability of an impossible event?
(a) 1(b) 0(c) 0.5(d) 2
4. A bag contains 3 red and 2 blue counters. One is picked at random. What is P(blue)?
(a) 3 ÷ 5(b) 1 ÷ 2(c) 2 ÷ 5(d) 2 ÷ 3
5. Two fair dice are rolled. What is the probability that the sum is 7?
(a) 1 ÷ 6(b) 1 ÷ 12(c) 1 ÷ 9(d) 1 ÷ 36
6. For two mutually exclusive events A and B, P(A or B) equals what?
(a) P(A) × P(B)(b) P(A) + P(B)(c) P(A) - P(B)(d) P(A) ÷ P(B)

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. A fair die is rolled once. Find P(an even number).
8. A card is drawn from a standard pack of 52 cards. Find P(a king).
9. The probability of rain tomorrow is 0.3. Find the probability that it does not rain.
10. A bag contains 6 red and 4 green counters. One is picked at random. Find P(red).
11. Two fair coins are tossed. Find P(at least one head).
12. A spinner has the numbers 1 to 8. Find P(a prime number).
13. The probability of an event is 0.05. Is the event impossible, unlikely or likely?
14. A die is rolled 60 times and a 6 appears 9 times. Find the experimental probability of rolling a 6.

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. A bag contains 4 white, 3 black and 3 grey marbles. One marble is picked at random. Find P(white).
16. Two fair dice are rolled. Find the probability that the sum of the scores is 9.
17. A card is drawn from a pack of 52 cards, replaced, and a second card is drawn. Find the probability of drawing two aces.
18. A fair coin and a fair die are thrown together. Find the probability of getting a head and a multiple of 3.
19. A box contains 5 red and 5 blue balls. Two balls are drawn without replacement. Find the probability that both are red.
20. The probability that a bus is late on any day is 0.25. In 200 days, how many days would you expect the bus to be late?

Answer Key

1. c) 1 ÷ 6
2. b) 1 ÷ 4
3. b) 0
4. c) 2 ÷ 5
5. a) 1 ÷ 6
6. b) P(A) + P(B)
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What is the probability of rolling a 3 on a fair die?

1 ÷ 6, option (c) in this worksheet (Q1).

What is the probability of two heads in two tosses?

1 ÷ 4, option (b) in this worksheet (Q2).

What is the probability of an impossible event?

0, option (b) in this worksheet (Q3).

Stuck on a similar problem? Clear your next doubt instantly with the Doubt Solver.
Browse more free worksheets for IGCSE Year 11.

Related Worksheets

Also send a probability question to the Doubt Solver.