Probability worksheet — GCSE Higher

1.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.

2.A pack contains 6 cards, numbered 1 to 6. A card is drawn at random from the pack, and a fair coin is flipped. Work out the probability of drawing an even-numbered card and the coin landing on tails.

3.Spinner E has 4 equal sections, numbered 1 to 4. Spinner F has 6 equal sections, numbered 1 to 6. Both spinners are spun once. Work out the probability of getting at least one 3.

4.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.

5.The probability that Isla answers a quiz question correctly is 0.8. She answers three questions, and her answers are independent of each other. Work out the probability that she answers all three correctly.

6.A basketball player has a free-throw success probability of 0.75. She wants to expect to score 60 successful free throws. Work out how many free throws she needs to attempt.

7.Two fair spinners are each numbered 1, 2 and 3. Priya spins both spinners together and records the two numbers as a pair, listing every possible outcome systematically in a grid. Work out the probability that the two numbers are the same.

8.Priya spins a fair spinner with P(red) = 0.3, and separately flips a fair coin with P(heads) = 0.5. Using a tree diagram, work out the probability that she gets red AND heads.

9.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.

10.A school surveys 60 pupils. 32 say they walk to school, 24 say they cycle to school, and 12 say they do both, on different days. The rest travel only by car. One of the 60 pupils is chosen at random. Work out the probability that this pupil travels only by car.

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

12.A factory makes bolts on two machines. Machine A makes 60% of the bolts and machine B makes the other 40%. 5% of the bolts made by machine A are faulty and 10% of the bolts made by machine B are faulty. A bolt is picked at random from one day's production. Work out the probability that it was made by machine B and is faulty. Give your answer as a decimal.

13.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.

14.In a survey of 200 households, 120 have a garden and 80 own a dog. 54 of the households have a garden and own a dog. Work out the probability that a household owns a dog given that it has a garden, and compare it with the probability that a household picked from the whole survey owns a dog.

15.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.