Probability worksheet — GCSE Foundation

1.Two ordinary fair dice are rolled, one after the other. Work out the probability that the first dice shows a 6 and the second dice shows an even number.

2.A bag contains 5 red counters and 3 blue counters. A counter is taken at random, its colour is noted, and it is put back in the bag before a second counter is taken at random. Work out the probability that both counters are the same colour.

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

4.One card is taken at random from an ordinary pack of 52 playing cards. 26 of the cards are red. Work out the probability that the card is red. Give your answer as a percentage.

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

6.A box contains 1 white bead, 4 purple beads and 4 red beads. One bead is taken at random from the box. Work out the probability that the bead is white or purple.

7.The probability that Oliver's train is delayed on any morning is 0.3. Work out the probability that his train is not delayed.

8.Four pupils each flip the same coin a number of times and record the results. Sam flips it 40 times and gets 24 heads. Priti flips it 25 times and gets 10 heads. Leo flips it 20 times and gets 9 heads. Fatima flips it 15 times and gets 6 heads. Combine all four pupils' results to estimate the probability that the coin lands on heads.

9.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.

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.The numbers 1 to 10 are each written on a card. Set A is the set of multiples of 3 from 1 to 10 and set B is the set of even numbers from 1 to 10. Work out how many of the numbers from 1 to 10 are in set A but not in set B.

12.A table shows how two Year 10 classes did in a spelling test. In class A, 18 out of 24 pupils passed. In class B, 21 out of 30 pupils passed. Which class had the greater proportion of pupils passing?

13.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.

14.A bag contains counters that are red, blue or green only. The probability that a counter taken at random is not red is 0.8. The bag contains 25 counters in total. Work out how many of the counters are red.

15.A sorting office processes 2,000 letters addressed to one postcode area in a week. The probability that a letter is a bill is 0.15. Work out how many of the letters you would expect to be bills.