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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 · Non-calculator · 15 questions

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1.The probability that a machine completes a task successfully is 0.85. Work out the probability that the machine does not complete the task successfully.
(a)0.85
(b)0.15
(c)0.25
(d)0.5
2.At a tombola stall, each ticket wins a toy, wins a sweet or wins nothing, and no ticket can win more than one of these. The probability that a ticket wins a toy is 0.15 and the probability that it wins a sweet is 0.4. Work out the probability that a ticket wins neither a toy nor a sweet.
(a)0.55
(b)0.45
(c)0.6
(d)0.85
3.The probability that the Hughes family go away during the summer holidays is 3/7. Work out the probability that they do not go away during the summer holidays.
(a)4/7
(b)1/7
(c)3/7
(d)1/2
4.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
5.Each turn of a game ends in a win, a draw or a loss, and no turn can end in more than one of these. The probability of a win is 1/4 and the probability of a draw is 1/3. Work out the probability of a loss.
(a)5/12
(b)5/7
(c)1/12
(d)7/12
6.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
7.In a game, Freddie says the probability of winning is 0.45, the probability of drawing is 0.3 and the probability of losing is 0.35, and that all three of his probabilities are correct. Which statement about Freddie's probabilities is correct?
(a)No — the three probabilities sum to 1.10, over 1.
(b)Yes — each probability lies between 0 and 1.
(c)Yes — the three outcomes are mutually exclusive.
(d)Yes — winning has the highest single probability.
8.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
9.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
10.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
11.A card is taken at random from an ordinary pack of 52 playing cards. The pack contains 4 aces and 4 kings. Work out the probability that the card is an ace or a king.
(a)16/52
(b)8/52
(c)4/52
(d)1/52
12.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%
13.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
14.A jar contains counters that are pink, gold or grey only. The probability that a counter taken at random is pink is 0.2 and the probability that it is gold is 0.45. The jar contains 60 counters in total. Work out the number of grey counters.
(a)12
(b)39
(c)27
(d)21
15.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

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