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. 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
2.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
3.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
4.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
5.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
6.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
7.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.
(a)1/6
(b)1/2
(c)1/4
(d)1/8
8.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
9.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
10.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.
(a)1/6
(b)6/11
(c)1/7
(d)7/36
11.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
12.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
13.A raffle has two independent draws. In the first, a winning ticket is picked at random from 5 red tickets and 3 blue tickets. In the second, a winning number is picked using a fair spinner with 4 equal sections, numbered 1 to 4. Work out the probability that the first winning ticket is blue and the second winning number is greater than 2.
(a)5/16
(b)1/2
(c)3/8
(d)3/16
14.Spinner C has 3 equal sections, numbered 2, 3 and 5. Spinner D has 6 equal sections, numbered 1 to 6. Both spinners are spun once, and the two numbers are multiplied together. Work out the probability that the product is a multiple of 5.
(a)4/9
(b)1/3
(c)1/9
(d)1/2
15.A fair coin is flipped and a fair five-sided spinner, labelled 1 to 5, is spun. All the outcomes are listed as pairs, such as (H, 3). Work out the probability that the outcome is a tail and an odd number.
(a)1/2
(b)3/5
(c)1/10
(d)3/10

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