Probability worksheet — GCSE Foundation

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

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

3.Two fair coins are thrown together 400 times. Work out how many of the 400 throws you would expect to give one head and one tail.

4.The probability that Priya's dentist appointment overruns is 0.35. Work out the probability that it does not overrun.

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

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

7.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.

8.A fair six-sided dice is rolled 300 times. Work out how many more times you would expect it to land on an even number than on a six.

9.A spinner lands on red, on blue or on green, and it cannot land on more than one colour at a time. The probability that it lands on red is 0.3 and the probability that it lands on blue is 0.5. Work out the probability that it lands on red or on blue.

10.A garage tested 200 cars in one week. 70% of the cars were more than 3 years old and the rest were 3 years old or less. Of the cars more than 3 years old, 1 in 4 failed the test. 12 of the cars that were 3 years old or less failed the test. Work out how many of the 200 cars failed the test altogether.

11.A fair six-sided dice is rolled 150 times. The table shows how many times each number came up: 1 came up 22 times, 2 came up 27 times, 3 came up 24 times, 4 came up 34 times, 5 came up 21 times and 6 came up 22 times. The theoretical probability of each number is 1/6. Which number is most over-represented compared with its theoretical probability?

12.A bag contains 45 sweets. 18 of the sweets are lemon flavour and the rest are orange. A sweet is taken at random, its flavour is recorded, and it is put back in the bag. This is repeated 200 times. Work out how many times you would expect an orange sweet to be taken.

13.Leo flips a fair coin twice. He makes a list of every possible result of the two flips, writing down what the first flip lands on and then what the second flip lands on. Work out how many of the results in his list contain at least one tail.

14.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.

15.A school trip took 200 pupils to a museum, travelling either by coach or by minibus. A frequency tree records the trip: 150 pupils travelled by coach, split into 90 in Year 8 and the rest in Year 9. All the pupils who travelled by minibus were in Year 8. Work out the total number of Year 8 pupils on the trip.