Possibility spaces for single and combined events worksheet — GCSE Foundation

1.A small pack contains 5 cards, numbered 1 to 5. One card is drawn at random from the pack, and a fair coin is flipped. Every outcome is listed as a pair, such as (3, H). Work out how many equally likely outcomes there are in total.

2.Spinner E has 4 equal sections, numbered 1 to 4. Spinner F has 6 equal sections, numbered 1 to 6. Both spinners are spun once. Work out the probability of getting at least one 3.

3.A raffle has two independent draws. In the first, a winning ticket is picked at random from 5 red tickets and 3 blue tickets. In the second, a winning number is picked using a fair spinner with 4 equal sections, numbered 1 to 4. Work out the probability that the first winning ticket is blue and the second winning number is greater than 2.

4.Spinner A has 4 equal sections, numbered 1, 2, 3 and 4. Spinner B has 3 equal sections, coloured red, red and blue. Both spinners are spun once. Work out the probability of getting an even number on Spinner A and red on Spinner B.

5.At a school fête, a stall invites visitors to spin a fair spinner with 8 equal sections numbered 1 to 8, and separately toss a fair coin. A visitor wins a small prize only if the spinner lands on a multiple of 3 and the coin lands on heads. Work out the probability that a visitor wins a prize, giving your answer as a fraction in its simplest form.

6.Oliver flips three fair coins at the same time. Work out the probability that exactly two of the three coins land on heads.

7.A padlock code is formed by arranging three different digits chosen from 2, 3, 4 and 5, with no digit repeated. Work out how many different three-digit codes can be made.

8.A red fair dice and a blue fair dice are rolled together. Every outcome is listed as an ordered pair, red score then blue score. Work out the probability that the red score is less than the blue score.

9.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.

10.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.

11.Spinner A is numbered 1 to 3 and Spinner B is numbered 1 to 5. Both spinners are spun once, and every outcome is listed as a pair, one number from each spinner. Work out how many equally likely outcomes there are in total.

12.Jack rolls two ordinary fair dice and adds the two scores together. Work out the probability that the total is 6.

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

14.Spinner A has 4 equal sections, numbered 1, 2, 3 and 4. Spinner B has 5 equal sections, numbered 1, 2, 3, 4 and 5. Both spinners are spun once, and the two numbers are multiplied together. Work out the probability that the product is 12.

15.A fair coin is flipped and a fair three-sided spinner, labelled X, Y and Z, is spun. Every outcome is listed as a pair, such as (H, X). Work out the probability that the outcome is a head and Z.