Probability worksheet — GCSE Higher

1.A drawing pin is dropped many times and lands either point up or point down. The relative frequency of landing point up is recorded as the experiment goes on: after 50 drops it is 0.720, after 200 drops it is 0.665, and after 1000 drops it is 0.638. The pin is to be dropped a further 2000 times. Work out the best estimate of the number of times it will land point up.

2.A call centre finds that 40% of its calls are about billing. 35% of the calls about billing are dealt with in under five minutes. The centre takes 500 calls on Monday. Work out how many of Monday's calls you would expect to be about billing and dealt with in under five minutes.

3.A weather station records whether it rains each day for 40 days: it rains on 9 of the days and does not rain on the rest. A local forecaster claims that the probability of rain on any day is 0.3. Work out the relative frequency of rain from the recorded data.

4.A factory tests components from a large batch in which 6% are defective. Two components are selected at random, and the batch is large enough that the selections can be treated as independent. Given that at least one of the two components is defective, work out the probability that both are defective.

5.At a fun run, a raffle stall charges £1.50 per ticket. The probability that any one ticket wins a prize worth £8 is 0.12, and a losing ticket wins nothing. Nadia buys 25 tickets. Work out how much money Nadia should expect to lose in total.

6.A two-way table records how 130 pupils travel to school. 70 of the pupils are girls and the rest are boys. 42 of the girls walk to school and the rest of the girls cycle. 33 of the boys walk to school. Work out what fraction of the girls walk to school.

7.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.

8.At a fête, a game costs £3 to play. The probability of winning is 0.1, and each win pays out £20. 150 people play the game. Work out the fête's expected profit from the game.

9.A machine makes 4000 light bulbs a day and runs 5 days a week. Two inspectors test bulbs from this machine. Inspector A tests 40 bulbs and finds 4 faulty. Inspector B tests 500 bulbs and finds 30 faulty. Using the better of the two estimates, work out how many faulty bulbs the machine is expected to make in one week.

10.A charity fundraiser runs a game using a spinner with 5 equal sections numbered 1 to 5. A player wins a £4 prize if the spinner lands on 5, and wins nothing otherwise. It costs £1 to play, and the game is played 100 times during the fundraiser. Decide which statement correctly describes the game.

11.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.

12.A café offers 3 types of sandwich, cheese, ham and egg, and 4 types of drink, tea, coffee, juice and water. A customer chooses one sandwich and one drink at random. Work out the probability that the customer chooses egg and water.

13.A frequency tree records the results of 160 patients who took a new medicine. It splits them into those who reported side effects and those who did not. 15% of the patients reported side effects. Work out how many of the 160 patients did not report side effects.

14.A phone network sends automatic text alerts to customers. On average, 1,500 alerts are sent each day, and the probability that a customer replies 'STOP' to an alert is 0.18. Work out how many replies of 'STOP' the network should expect over a 30-day month.

15.In a class experiment a fair six-sided dice is rolled 60 times and lands on a six 14 times. The whole school then rolls the same fair dice 3000 times. Work out the best estimate of the number of sixes the school should expect.