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16.2 Sample space diagrams

16.2 Sample space diagrams

When you throw a fair dice there are six equally likely outcomes: 1, 2, 3, 4, 5 or 6.
When you spin a fair coin there are two equally likely outcomes:
heads (H) and tails (T). T + + + + + +
When you throw the dice and the coin together, there are 12 H + + + + + +
possible outcomes.
You can show all possible outcomes in a sample space diagram. 1 2 3 4 5 6
Each mark (+) shows one outcome. !ey are all equally likely.
To "nd the probability of a particular outcome, look for all the
possible ways of achieving it. T + + + + + +
!is diagram shows the outcomes for ‘a head and an even number’. H + + + + + +
1
3
!e probability of scoring a head and an even number is 12 = . 1 2 3 4 5 6
4
Worked example 16.2

One fair spinner has three sections marked with the numbers 1, 2 and 3.
1 2
Another fair spinner has five sections marked with the numbers 1, 2, 3, 4 and 5. 1 2 5 3
a Draw a sample space diagram to show all the possible outcomes. 3 4
b Work out the probability of scoring: i two 2s ii two odd numbers iii a total of 5.

a 3 + + + + +

2 + + + + +
1 + + + + +

1 2 3 4 5

1
b i 15 3 + + + + +
2 + + + + +

1 + + + + +

1 2 3 4 5

ii 6 2 3 + + + + +
=
15 5
2 + + + + +
1 + + + + +

1 2 3 4 5

iii 3 1 3 + + + + +
15 = 5
2 + + + + +

1 + + + + +

1 2 3 4 5

16 Probability 153