Probability worksheet — GCSE Foundation

1.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.

2.A fair coin is flipped three times. Work out the probability of getting at least one head.

3.The probability that Kofi passes his driving test on any attempt is 0.6, and each attempt is independent of the others. Work out the probability that he fails both his first two attempts.

4.Two ordinary fair dice are rolled. Work out the probability that the difference between the two scores is 1.

5.A fair six-sided dice is rolled once. Work out the probability that the score is greater than 4.

6.A frequency tree records 320 calls to a helpline. The calls first split into calls about billing and calls about technical support. Of the technical support calls, the probability that a call was resolved on the first contact is 0.75. If 180 technical support calls were resolved on the first contact, work out how many calls were about billing.

7.A charity bake sale tracked 240 items sold using a frequency tree. The first branch splits sales into 150 cake sales and 90 biscuit sales. Of the cake sales, 100 were bought by adults and the rest by children. Of the biscuit sales, 54 were bought by children. Each item sold for £1.20. Work out the total amount of money raised from sales to children.

8.The probability that a plant grown from a seed packet germinates is 7/10. Work out the probability that it does not germinate.

9.A bag contains 3 red beads and 7 blue beads. A bead is taken out at random and not put back. A second bead is then taken out at random. Work out the probability that the first bead is red and the second bead is also red.

10.The probability that Priya scores with a netball shot is 3/4. She takes two shots, and the shots are independent. Work out the probability that she scores with her first shot but misses her second shot.

11.A card is taken at random from an ordinary pack of 52 playing cards. The pack contains 4 aces and 4 kings. Work out the probability that the card is an ace or a king.

12.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.

13.A fair six-sided dice is rolled once. Write down the probability that the score is an even number.

14.A library recorded loans for 250 books over a week, using a frequency tree. The first branch splits the books into 160 fiction and 90 non-fiction. Of the fiction books, 112 were returned on time and the rest were returned late. All the non-fiction books were returned on time. Work out the probability that a book, chosen at random from the 250, was returned late. Give your answer as a fraction in its simplest form.

15.A survey asked 80 people to name their favourite drink. The table shows the results: Tea 20 people, Coffee 32 people, Juice 16 people, Water 12 people. Work out the percentage of people whose favourite drink was Coffee.