Printable · GCSE Higher · ages 14-16

Possibility spaces for single and combined events worksheet — GCSE Higher

Fifteen questions on "possibility spaces for single and combined events" — DfE statement P7. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Possibility spaces for single and combined events worksheet — GCSE Higher

Maths · GCSE Higher · P7 · Possibility spaces for single and combined events · 15 questions

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1.Two ordinary fair dice are rolled and the two scores are added together. Work out the probability that the total is a prime number.
(a)13/36
(b)19/36
(c)7/18
(d)5/12
2.Two ordinary fair dice are rolled and the two scores are multiplied together. Work out the probability that the product is odd.
(a)3/4
(b)1/2
(c)1/12
(d)1/4
3.Bag A contains 3 red balls and 2 blue balls. Bag B contains 1 red ball and 3 blue balls. One ball is taken at random from each bag. Work out the probability that both balls are red.
(a)4/9
(b)3/25
(c)17/20
(d)3/20
4.Jack rolls two ordinary fair dice and adds the two scores together. Work out the probability that the total is 6.
(a)5/36
(b)5/12
(c)4/36
(d)1/11
5.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.
(a)1/16
(b)1/4
(c)1/8
(d)3/16
6.A pack contains 6 cards, numbered 1 to 6. A card is drawn at random from the pack, and a fair coin is flipped. Work out the probability of drawing an even-numbered card and the coin landing on tails.
(a)1/8
(b)1/4
(c)1/12
(d)1/2
7.Spinner A has 4 equal sections, numbered 1, 2, 3 and 4. Spinner B has 3 equal sections, coloured red, red and blue. Both spinners are spun once. Work out the probability of getting an even number on Spinner A and red on Spinner B.
(a)1/3
(b)1/6
(c)1/4
(d)5/6
8.At a school fête, a stall invites visitors to spin a fair spinner with 8 equal sections numbered 1 to 8, and separately toss a fair coin. A visitor wins a small prize only if the spinner lands on a multiple of 3 and the coin lands on heads. Work out the probability that a visitor wins a prize, giving your answer as a fraction in its simplest form.
(a)1/2
(b)1/16
(c)1/4
(d)1/8
9.Spinner E has 4 equal sections, numbered 1 to 4. Spinner F has 6 equal sections, numbered 1 to 6. Both spinners are spun once. Work out the probability of getting at least one 3.
(a)3/8
(b)1/4
(c)5/12
(d)5/8
10.Oliver flips three fair coins at the same time. Work out the probability that exactly two of the three coins land on heads.
(a)4/8
(b)6/8
(c)3/8
(d)2/8
11.A café offers 3 types of sandwich, cheese, ham and egg, and 4 types of drink, tea, coffee, juice and water. A customer chooses one sandwich and one drink at random. Work out the probability that the customer chooses egg and water.
(a)1/7
(b)1/3
(c)1/4
(d)1/12
12.Two ordinary fair dice are rolled. Work out the probability that the difference between the two scores is 1.
(a)1/4
(b)1/6
(c)5/36
(d)5/18
13.Two fair five-sided dice, numbered 1 to 5, are rolled. Work out the probability that the two scores differ by at least 2.
(a)6/25
(b)12/25
(c)10/25
(d)13/25
14.Two ordinary fair dice are rolled. Work out the probability that both dice show the same score.
(a)1/3
(b)1/6
(c)1/36
(d)1/2
15.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.
(a)33/36
(b)4/36
(c)2/36
(d)3/36

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