Printable · GCSE Foundation · ages 14-16

Independent and dependent combined events worksheet — GCSE Foundation

Fifteen questions on "independent and dependent combined events" — DfE statement P8. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Independent and dependent combined events worksheet — GCSE Foundation

Maths · GCSE Foundation · P8 · Independent and dependent combined events · 15 questions

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1.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.
(a)1/15
(b)11/15
(c)2/15
(d)3/8
2.An ordinary fair dice is rolled twice. Work out the probability of getting at least one 5.
(a)30/36
(b)11/36
(c)25/36
(d)12/36
3.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.
(a)1/12
(b)3/50
(c)1/8
(d)2/9
4.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.
(a)1/25
(b)1/20
(c)2/5
(d)1/10
5.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.
(a)0.2
(b)0.1
(c)0.45
(d)0.9
6.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.
(a)0.16
(b)0.36
(c)0.24
(d)0.4
7.A drawer contains 4 red socks and 2 blue socks. Two socks are taken out at random, one after the other, without the first being put back. Work out the probability that both socks are the same colour.
(a)7/18
(b)2/5
(c)5/9
(d)7/15
8.The probability that Leo wakes up before his alarm is 0.35. The probability that his younger sister wakes up before her alarm, independently of Leo, is 0.28. Work out the probability that neither of them wakes up before their alarm.
(a)0.098
(b)0.63
(c)0.532
(d)0.468
9.A bag contains 5 yellow marbles and 3 blue marbles. Noah takes a marble at random, notes its colour and puts it back in the bag. He then takes a second marble at random. Work out the probability that the first marble is yellow and the second marble is blue.
(a)15/16
(b)9/64
(c)5/8
(d)15/64
10.The probability that it rains on a given morning is 0.3. If it rains, the probability that Priya's bus is late is 0.8. If it does not rain, the probability that her bus is late is 0.1. Work out the probability that her bus is late.
(a)0.27
(b)0.24
(c)0.31
(d)0.9
11.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.
(a)1/12
(b)1/36
(c)1/6
(d)1/2
12.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.
(a)0.0512
(b)0.8
(c)0.512
(d)0.64
13.A fair coin is flipped three times. Work out the probability of getting at least one head.
(a)1/2
(b)1/8
(c)7/8
(d)3/8
14.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.
(a)1/5
(b)1/10
(c)1/100
(d)19/100
15.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.
(a)0.09
(b)0.6
(c)0.9
(d)0.3

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