Sample Space Diagrams
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Either paper 3 marks
Ben spins a fair spinner with 8 equal sections numbered 1 to 8, and flips a fair coin.
(a)State the number of possible outcomes.
(b)Calculate the probability that he gets a head and a number greater than \(1\).
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Either paper 4 marks
A fair spinner has five sections, labelled A to E. The spinner is spun once.
(a)Complete these statements.
The spinner is most likely to land on section ________
The spinner is equally likely to land on sections ________ and ________
(b)Two different spinners are spun. One spinner has sections labelled with letters. The other spinner has sections labelled with numbers.
Here is a list of all the possible outcomes.
S 1, U 1, P 1, R 1, S 2, U 2, P 2, R 2, S 3, U 3, P 3, R 3
Show the possible sections on the two spinners.
Letter spinner: ________
Number spinner: ________
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Either paper 4 marks
Two fair six-sided dice are rolled and the two scores are added together.
The sample space diagram shows every possible total. The score on the first die is down the side and the score on the second die is along the top.
+ 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 (a)Find the probability that the total is \(4\).
(b)Find the probability that the total is greater than \(9\).
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Either paper 4 marks
Spinner A has four equal sections numbered \(5\), \(6\), \(7\) and \(8\).
Spinner B has four equal sections numbered \(6\), \(7\), \(8\) and \(9\).
Both spinners are spun once and the two numbers are added together. Part of the sample space diagram has been filled in.
+ 6 7 8 9 5 11 12 13 14 6 12 13 14 15 7 13 14 15 16 8 (a)Complete the sample space diagram.
(b)Find the probability that the total is \(16\).
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Either paper 4 marks
Two fair six-sided dice are rolled. The smaller score is subtracted from the larger one, so the difference is never negative.
The sample space diagram shows every possible difference. The score on the first die is down the side and the score on the second die is along the top.
Difference 1 2 3 4 5 6 1 0 1 2 3 4 5 2 1 0 1 2 3 4 3 2 1 0 1 2 3 4 3 2 1 0 1 2 5 4 3 2 1 0 1 6 5 4 3 2 1 0 (a)Calculate the probability that the difference is \(2\).
(b)Calculate the probability that the difference is greater than \(2\).
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Either paper 5 marks
Omar spins two spinners and multiplies the two numbers together.
The first spinner has the numbers \(1\), \(2\), \(3\) and \(4\) on it. The second spinner has the numbers \(1\), \(5\) and \(9\) on it.
The table shows every possible product.
1 5 9 1 1 5 9 2 2 10 18 3 3 15 27 4 4 20 36 Both spinners are fair.
(a)State the number of possible outcomes.
(b)Work out the probability that the product is an even number.
(c)Work out the probability that the product is greater than \(5\).
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Either paper 5 marks
In a game, two fair spinners are spun.
Spinner A
Spinner B
If the numbers the arrows land on are different, the score is the lower number.
If the numbers the arrows land on are the same, the score is 0.
Part of the table of possible scores is shown.
Spinner B Spinner A 1 4 1 5 5 4 1 0 4 6 1 1 5 (a)Complete the table to show the possible scores.
(b)Write down the probability that the score is an odd number.
(c) The same game is played using spinners C and D. The numbers on spinner C are shown. Spinner D has two sections labelled p and q. All the numbers on spinner D are greater than 0. Spinner C Spinner D The table shows some of the possible scores.
Write the missing numbers p and q on spinner D.Spinner D Spinner C 9 1 q p 4 4 1 10 9 1 8 8 8 1 7 -
Either paper 6 marks
A number is picked at random from the first three positive odd numbers.
A number is picked at random from the first four positive odd numbers.
The two numbers are multiplied to get a score.
Here is part of the table of possible scores.
× 3 5 7 1 1 3 5 7 9 15 21 5 5 25 (a)Complete the table.
(b)What is the probability that the score is a square number? Give your answer as a fraction in its simplest form.
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Either paper 3 marks
Grace spins a fair spinner with 8 equal sections numbered 1 to 8, and flips a fair coin.
(a)Write down the number of possible outcomes.
(b)Work out the probability that she gets a head and a number greater than \(5\).
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Either paper 4 marks
A fair spinner has five sections, labelled A to E. The spinner is spun once.
(a)Complete these statements.
The spinner is most likely to land on section ________
The spinner is equally likely to land on sections ________ and ________
(b)Two different spinners are spun. One spinner has sections labelled with letters. The other spinner has sections labelled with numbers.
Here is a list of all the possible outcomes.
V 1, Q 1, S 1, U 1, V 2, Q 2, S 2, U 2, V 3, Q 3, S 3, U 3
Show the possible sections on the two spinners.
Letter spinner: ________
Number spinner: ________
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(a) \(16\)
(b) \(\frac{7}{16}\) -
(a) Most likely: section E. Equally likely: sections A and D.
(b) Letter spinner: S, U, P, R. Number spinner: 1, 2, 3. -
(a) \(\frac{1}{12}\)
(b) \(\frac{1}{6}\) -
(a) The bottom row reads 14, 15, 16, 17
(b) \(\frac{1}{8}\) -
(a) \(\frac{2}{9}\)
(b) \(\frac{1}{3}\) -
(a) \(12\)
(b) \(\frac{1}{2}\)
(c) \(\frac{7}{12}\) -
(a) Row 5: 1, 4, 1, 0. Row 4: 1, 0, 1, 4. Row 6: 1, 4, 1, 5.
(b) \(\frac{7}{12}\)
(c) \(p = 8\) and \(q = 7\) -
(a) Missing number at the top: 1. Missing number at the side: 3. Missing scores, reading along the rows from the top: 3, 15, 35
(b) \(\frac{1}{4}\) -
(a) \(16\)
(b) \(\frac{3}{16}\) -
(a) Most likely: section B. Equally likely: sections A and E.
(b) Letter spinner: V, Q, S, U. Number spinner: 1, 2, 3.
Takes a couple of seconds the first time a sheet is made.