Probability worksheet — GCSE Higher

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

2.A box contains 9 red balls and 11 green balls. Two balls are taken out at random, one after the other, without being replaced. Given that both balls taken out are the same colour, work out the probability that both balls are red.

3.Spinner C has 3 equal sections, numbered 2, 3 and 5. Spinner D has 6 equal sections, numbered 1 to 6. Both spinners are spun once, and the two numbers are multiplied together. Work out the probability that the product is a multiple of 5.

4.180 gardeners at an allotment were asked whether they grow vegetables organically. 100 of the gardeners are on the north plots. 64 of the north-plot gardeners grow organically. 30 of the south-plot gardeners do not grow organically. Work out how many south-plot gardeners grow organically.

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

6.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.

7.A company has 400 employees. 150 of them work part time and 160 of them cycle to work. Working part time and cycling to work are independent. Work out how many of the employees you would expect both to work part time and to cycle to work.

8.A survey of 60 readers records: 21 read only fiction, 17 read only non-fiction, 14 read both, and the rest read neither. Work out the probability that a randomly chosen reader reads exactly one of the two types, giving your answer as a fraction in its simplest form.

9.250 people took a theory test at one test centre. 150 of them had taken a preparation course and the rest had not. 120 of those who had taken the course passed and 50 of those who had not taken the course passed. One of the people who passed is picked at random. Work out the probability that this person had taken the preparation course.

10.A fair spinner has 8 equal sections: 5 are red and 3 are blue. Freya spins it twice, and each spin is independent of the other. Work out the probability that she gets one red and one blue in the two spins, in either order.

11.Two fair five-sided dice, numbered 1 to 5, are rolled. Work out the probability that the two scores differ by at least 2.

12.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.

13.Two fair six-sided dice are rolled and the two scores are added together. Given that at least one of the dice shows a 5, work out the probability that the total is 8.

14.A bag contains 5 letter tiles spelling the word MATHS, with one letter on each tile. Two tiles are drawn at random, one after the other, without the first tile being put back. Work out the probability that both tiles drawn are consonants.

15.The probability that a seed fails to germinate is 1/5. Three seeds are planted independently. Work out the probability that at least one of the three seeds germinates.