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.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.
(a)9/25
(b)6/25
(c)4/25
(d)3/10
2.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.
(a)3/4
(b)4/5
(c)16/25
(d)3/5
3.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
4.A spinner has equal sections, and the probability that it lands on blue in a single spin is 1/4. It is spun twice, and the two spins are independent. Work out the probability that it lands on blue on both spins.
(a)1/16
(b)1/2
(c)1/4
(d)1/8
5.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
6.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
7.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
8.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
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 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.
(a)3/4
(b)9/16
(c)3/16
(d)1/2
11.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
12.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
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.
(a)12/125
(b)4/5
(c)64/125
(d)124/125
14.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
15.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

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