Probability worksheet — GCSE Higher

1.A bag contains 5 yellow marbles and 3 blue marbles. Noah takes a marble at random, notes its colour and puts it back in the bag. He then takes a second marble at random. Work out the probability that the first marble is yellow and the second marble is blue.

2.The universal set is {1, 2, 3, ..., 15}. A = {multiples of 3}. Work out n(A′), the number of elements not in A.

3.In a game, Zara says the probability of scoring is 3/8, the probability of missing is 5/12 and the probability of a rebound is 1/6, and that these are the only three outcomes. Is Zara correct that her three probabilities are valid?

4.The probability that Isla answers a quiz question correctly is 0.8. She answers three questions, and her answers are independent of each other. Work out the probability that she answers all three correctly.

5.Two events are independent. The first has probability 2/5 and the second has probability 1/3. Work out the probability that both events happen.

6.At a sports club, the numbers of members who play tennis and badminton are: 50 members play tennis, 40 members play badminton, and 18 members play both tennis and badminton. A member who plays tennis is chosen at random. Work out the probability that this member also plays badminton.

7.In a group of 50 people, 32 own a car, 20 own a bicycle and 9 own both a car and a bicycle. A person who owns a bicycle is picked at random. Work out the probability that this person does not own a car.

8.At a youth club, 65 members are asked which sports they play. 27 play football, 21 play basketball, and 9 play both. Work out the number of members who play neither sport.

9.A doctors' surgery has 400 patients. 3 in every 10 of the patients are over 65 years old. 90 of the patients over 65 and 70 of the patients aged 65 or under had a flu jab. One of the patients who had a flu jab is picked at random. Work out the probability that this patient is over 65.

10.Two ordinary fair dice are rolled and the two scores are added together. Work out the probability that the total is a prime number.

11.Two fair six-sided dice are rolled and the two scores are added together. Given that at least one of the dice shows a 5, work out the probability that the total is 8.

12.180 people entered a fun run. A frequency tree splits them into 108 adults and the rest children. It then splits each of those groups into those who finished and those who did not. 99 of the adults finished, and 153 of the 180 people finished altogether. Work out how many children did not finish.

13.A box holds 5 blue pens and 7 black pens. Two pens are taken at random, one at a time, and are not put back. The first pen taken is black. Work out the probability that the second pen taken is blue.

14.A factory finds that the probability a randomly chosen light bulb is defective is 0.035. In a batch of 4,000 bulbs, work out how many bulbs you would expect to work correctly.

15.A Venn diagram shows two sets, P and Q, inside a universal set. n(P) = 34, n(Q) = 27, n(P ∩ Q) = 11, and n(ξ) = 90, where ξ is the universal set. Work out n((P ∪ Q)′), the number of elements in neither P nor Q.