Page 154 - MAT KS3 Y8 Cambridge CheckPoint

15.3 Listing all possible outcomes

15.3 Listing all possible outcomes

blue dice
If you throw two dice together, what is the
probability of getting a double six? 1 2 3 4 5 6
To find out, you need a list of all the possible outcomes. 1 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6
You could use a table.
2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6
Suppose you have a red dice and a blue one.
Draw the table like this. red 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6
dice 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6
This shows that there are 36 mutually exclusive outcomes. 4
If the dice are thrown fairly, the outcomes are all equally likely. 5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6
The probability of a double six is 1 . 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6
36

Outcomes are mutually exclusive if
only one of them can happen.

Worked example 15.3

Two fair dice are thrown and the scores are added.
What is the probability of scoring a total of:
a 8 b less than 8 c 8 or more?

This table shows the possible totals. This table is based on the outcome table above.
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
5
a The five 8s have been circled in the table.
36
b 21 = 7 There are 21 numbers in the table less than 8.
36 12
15 5
c = There are 15 numbers that are 8 or more.
36 12

✦ Exercise 15.3

1 Xavier throws two fair dice together. What is the probability of scoring:
a two fours b no fours c exactly one four?

2 Mia throws two fair dice and adds the scores.
a What is the smallest possible total?
b What is the largest possible total? There are eleven possible totals so the
1
c What is wrong with Mia’s argument probability of a total of 3 is 11 .
on the right?
152 15 Probability