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Probabilities of exhaustive events sum to one worksheet — GCSE Foundation

Fifteen questions on "probabilities of exhaustive events sum to one" — DfE statement P4. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Probabilities of exhaustive events sum to one worksheet — GCSE Foundation

Maths · GCSE Foundation · P4 · Probabilities of exhaustive events sum to one · 15 questions

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1.A bag contains counters that are red, blue or green only. The probability that a counter taken at random is not red is 0.8. The bag contains 25 counters in total. Work out how many of the counters are red.
(a)4
(b)8
(c)20
(d)5
2.The probability that Oliver's train is delayed on any morning is 0.3. Work out the probability that his train is not delayed.
(a)0.5
(b)0.97
(c)0.3
(d)0.7
3.At a fun run, each runner finishes, retires or is disqualified, and cannot do more than one of these. The probability that a runner finishes is 68.5% and the probability that a runner retires is 24.75%. Work out the probability, as a percentage, that a runner is disqualified.
(a)6.75%
(b)93.25%
(c)75.25%
(d)31.50%
4.A card is taken at random from an ordinary pack of 52 playing cards. The probability that the card is a diamond is 1/4. Work out the probability that the card is not a diamond.
(a)1/2
(b)3/4
(c)1/4
(d)3/52
5.At a coffee shop, each customer buys tea, coffee, water or juice, and never more than one of these. The probability that a customer buys tea is 0.36 and the probability that they buy juice is 0.04. The probability that a customer buys coffee is three times the probability that they buy water. Work out the probability that a customer buys water.
(a)0.15
(b)0.30
(c)0.60
(d)0.45
6.A bag contains 2 white counters and 8 black counters. One counter is taken at random from the bag. Work out the probability that the counter is not black.
(a)1/5
(b)1/2
(c)4/5
(d)1/4
7.A box contains counters that are silver, bronze or copper only. The probability that a counter taken at random is silver is 1/2 and the probability that it is bronze is 1/8. The box contains 64 counters in total. Work out the number of copper counters.
(a)8
(b)40
(c)24
(d)32
8.A charity raffle has three types of ticket: winning, near-miss and losing, and every ticket is exactly one of these. The probability that a ticket is winning is 1/8 and the probability that it is a near-miss is 1/4. Work out the probability that a ticket is losing.
(a)5/8
(b)3/8
(c)3/4
(d)7/8
9.At a quiz night, each team's result is a win, a draw or a loss, and no team can have more than one of these results. The probability that a team wins is 42% and the probability that a team draws is 18.5%. Work out the probability, as a percentage, that a team does not win and does not draw.
(a)58.0%
(b)60.5%
(c)39.5%
(d)81.5%
10.The probability that a plant grown from a seed packet germinates is 7/10. Work out the probability that it does not germinate.
(a)3/10
(b)10/3
(c)7/10
(d)3/7
11.A bag contains beads that are exactly one of red, white or black. The probability of taking a red bead is 3/10 and the probability of taking a white bead is 1/4. Work out the probability of taking a bead that is red or white.
(a)1/2
(b)9/20
(c)11/20
(d)3/40
12.The probability that it rains in Manchester tomorrow is 1/12. Work out the probability that it does not rain in Manchester tomorrow.
(a)11/11
(b)11/12
(c)1/11
(d)1/12
13.At a school fete, each raffle ticket wins a prize, wins a voucher or wins nothing, and no ticket can win more than one of these. The probability that a ticket wins a prize is 0.4 and the probability that it wins a voucher is 0.35. Work out the probability that a ticket wins a prize or a voucher.
(a)0.75
(b)0.14
(c)0.05
(d)0.25
14.A spinner can land on red, blue, green or yellow. The probability that it lands on red is 0.24 and the probability that it lands on yellow is 0.16. The probabilities of landing on blue and on green are equal, and each is called x. Work out the value of x.
(a)0.30
(b)0.15
(c)0.60
(d)0.38
15.A spinner can land on red, blue, green or yellow, and it cannot land on more than one colour. The probability that it lands on red is 0.05 and the probability that it lands on yellow is 0.35. The probability that it lands on blue is twice the probability that it lands on green. Work out the probability that it lands on green.
(a)0.4
(b)0.6
(c)0.2
(d)0.3

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