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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.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%
2.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
3.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
4.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.
5.The probability that Priya's dentist appointment overruns is 0.35. Work out the probability that it does not overrun.
(a)1.35
(b)0.35
(c)0.65
(d)0.75
6.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
7.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
8.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
9.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
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 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
12.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
13.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
14.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
15.A spinner lands on one of four colours: amber, black, cyan or damson. The probability it lands on amber is 0.18, on black is 0.22 and on cyan is 0.24. Work out the probability that it lands on amber or damson.
(a)0.54
(b)0.36
(c)0.82
(d)0.64

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