Probability worksheet — GCSE Higher

1.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.

2.150 pupils are asked about swimming and cycling, and the results are recorded on a frequency tree. The first pair of branches splits the 150 pupils into 90 who swim and 60 who do not swim. Of the 90 who swim, 54 also cycle. Of the 60 who do not swim, 18 cycle. Work out P(S ∩ C), the probability that a pupil, chosen at random, swims and cycles. Give your answer as a fraction in its simplest form.

3.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.

4.Two cards are dealt one after the other from an ordinary pack of 52 playing cards. The first card is not put back before the second is dealt. The pack contains 4 aces. Work out the probability that neither card is an ace. Give your answer as a product of two fractions.

5.An ordinary pack of 52 playing cards contains 13 hearts. One card is taken at random from the pack. Work out the probability that the card is not a heart. Give your answer as a percentage.

6.Harry plays a game in which he flips a fair coin and rolls an ordinary fair dice. He wins a prize only if the coin shows heads and the dice shows a 6. Work out the probability that Harry wins a prize.

7.At a garden centre, 3/5 of the plants for sale are perennials. 1/4 of the perennials are in flower. Work out the probability that a plant picked at random from the garden centre is a perennial and is in flower.

8.A bag contains beads that are exactly one of red, white or black. The probability of taking a red bead is 3/10 and the probability of taking a white bead is 1/4. Work out the probability of taking a bead that is red or white.

9.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.

10.A drawer contains 4 red socks and 2 blue socks. Two socks are taken out at random, one after the other, without the first being put back. Work out the probability that both socks are the same colour.

11.Two ordinary fair dice are rolled. Work out the probability that both dice show the same score.

12.A spinner can land on red, blue, green or yellow, and it cannot land on more than one colour. The probability that it lands on red is 0.05 and the probability that it lands on yellow is 0.35. The probability that it lands on blue is twice the probability that it lands on green. Work out the probability that it lands on green.

13.An ordinary fair dice is rolled twice. Work out the probability of getting at least one 5.

14.Two ordinary fair dice are rolled, one after the other. Work out the probability that the first dice shows a 6 and the second dice shows an even number.

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