Probability worksheet — GCSE Foundation

1.On the probability scale from 0 to 1, which word best describes an event with probability 0.9?

2.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.

3.80 people are asked whether they drink tea and whether they drink coffee, and the results are recorded on a frequency tree. The first pair of branches splits the 80 people into 50 tea drinkers and 30 non-tea-drinkers. Of the 50 tea drinkers, 32 also drink coffee. Of the 30 non-tea-drinkers, 6 drink coffee. Work out n(T ∩ C), the number of people who drink both tea and coffee.

4.A clinic recorded 300 booked appointments using a frequency tree. The first branch splits them into 210 adult appointments and the rest child appointments. Of the adult appointments, 189 were attended and the rest were missed. Of the child appointments, 81 were attended. Work out the probability that a booked appointment, chosen at random from the 300, was missed. Give your answer as a fraction in its simplest form.

5.A garden centre tests 250 packets of seeds for germination, recording the results on a frequency tree. 68% of the 250 packets germinated successfully, and the rest did not. Work out how many packets germinated successfully.

6.A quality inspector tests 145 light bulbs and finds that 33 are faulty. Work out the relative frequency of a bulb being faulty, as a percentage correct to 1 decimal place.

7.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.

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

9.A tree diagram shows two rounds of a game, played independently. On each round, the probability of losing is 0.7 and the probability of winning is 0.3. Work out the probability of losing both rounds.

10.A fair four-sided dice, numbered 1 to 4, is rolled twice. Every outcome is listed as an ordered pair, first roll then second roll, such as (2, 3). Work out how many different outcomes are in the list.

11.Spinner P and Spinner Q are each fair and have 5 equal sections, numbered 1 to 5. Both spinners are spun once, and every outcome is listed as an ordered pair, Spinner P then Spinner Q, such as (2, 4). Work out how many of the outcomes have the score on Spinner P less than the score on Spinner Q.

12.A train company runs 25 trains a day, every day. The probability that any one train is late is 0.08. Work out how many late trains the company should expect over a period of 4 weeks.

13.A fair six-sided dice is rolled 90 times. Work out how many more times you would expect it to land on a number less than 4 than on a 6.

14.A fair coin is flipped again and again. After the first 10 flips there have been 7 heads. After 1000 flips there have been 528 heads. Which statement best describes what these results show?

15.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.