Independent and dependent combined events worksheet — GCSE Higher

1.Five raffle tickets numbered 1 to 5 are in a bag. Two tickets are drawn one after the other and the first is not put back. Work out the probability that ticket 1 is drawn first and ticket 2 is drawn second.

2.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.

3.A fair spinner is divided into 5 equal sections, 2 labelled win and 3 labelled lose. Zara spins it twice, and the two spins are independent. Work out the probability that she wins on the first spin and loses on the second spin.

4.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.

5.A bag contains 3 red beads and 7 blue beads. A bead is taken out at random and not put back. A second bead is then taken out at random. Work out the probability that the first bead is red and the second bead is also red.

6.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.

7.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.

8.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.

9.Two events are independent. The first has probability 2/5 and the second has probability 1/3. Work out the probability that both events happen.

10.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.

11.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.

12.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.

13.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.

14.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.

15.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.