Printable · GCSE Foundation · ages 14-16

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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Probabilities of exhaustive events sum to one worksheet — GCSE Foundation

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

MathsUKwww.geekhero.co.uk

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.Isla travels to school by bus, by bike, on foot or by car, and never by more than one of these on the same day. The probability that she travels by bus is 0.2, the probability that she travels by bike is 0.3 and the probability that she travels on foot is 0.1. Work out the probability that she travels to school by bus, by bike or on foot.
(a)0.4
(b)0.006
(c)0.6
(d)0.5
3.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
4.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
5.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%
6.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
7.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
8.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
9.In a game, Zara says the probability of scoring is 3/8, the probability of missing is 5/12 and the probability of a rebound is 1/6, and that these are the only three outcomes. Is Zara correct that her three probabilities are valid?
(a)Yes, because 3/8 + 5/12 + 1/6 = 1
(b)Yes, because all three fractions are between 0 and 1
(c)No, because 3/8 + 5/12 + 1/6 = 3/4
(d)No, because 3/8 + 5/12 + 1/6 = 23/24
10.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
11.A spinner lands on red, on blue or on green, and it cannot land on more than one colour at a time. The probability that it lands on red is 0.3 and the probability that it lands on blue is 0.5. Work out the probability that it lands on red or on blue.
(a)0.8
(b)0.2
(c)0.15
(d)0.4
12.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.
13.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
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

Build your own mix at the worksheet builder.