Independent and dependent combined events worksheet — GCSE Higher

1.A red dice and a blue dice are rolled. Both dice are ordinary and fair. Work out the probability of getting a 1 on the red dice and a 2 on the blue dice.

2.Two cards are dealt one after the other from an ordinary pack of 52 playing cards. The first card is not put back before the second is dealt. The pack contains 4 aces. Work out the probability that neither card is an ace. Give your answer as a product of two fractions.

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

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

5.Harry plays a game in which he flips a fair coin and rolls an ordinary fair dice. He wins a prize only if the coin shows heads and the dice shows a 6. Work out the probability that Harry wins a prize.

6.In Manchester the probability of rain on any day in November is taken to be 0.3, and whether it rains on one day is independent of whether it rains on the next. Work out the probability that it rains on both the 10th and the 11th of November.

7.A basketball player takes two free throws, and the throws are independent. The probability of scoring on each throw is 0.6, and the probability of missing is 0.4. Work out the probability that she scores exactly one of the two throws.

8.A bag contains 5 red counters and 5 green counters. Three counters are taken out one at a time and are not put back. Work out the probability that all three counters are red.

9.The probability that Priya scores with a netball shot is 3/4. She takes two shots, and the shots are independent. Work out the probability that she scores with her first shot but misses her second shot.

10.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.

11.The probability that a component is faulty is 1/10. Two components are tested independently. Work out the probability that at least one of the two components is faulty.

12.A charity tombola has 30 tickets, 6 of which win a prize. Priya buys a ticket at random and does not return it. Her friend Tom then buys a second ticket at random from the remaining tickets. Work out the probability that both Priya and Tom win a prize.

13.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.

14.On Amelia's walk to school there are two sets of traffic lights. The probability that the first set is green when she reaches it is 0.4. The probability that the second set is green when she reaches it is 0.5. The two sets work independently of each other. Work out the probability that both sets are green.

15.The probability that Kofi passes his driving test on any attempt is 0.6, and each attempt is independent of the others. Work out the probability that he fails both his first two attempts.