The addition rule is simple for mutually exclusive events. Say I want to know the probability of a ‘1’ or a ‘2’ occurring when I throw a die. It states that:
Probability of ‘1’ or ‘2’ occurring
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= probability of 1 occurring + probability of 2 occurring.
This is logical when you think about it.
For events that are not mutually exclusive, it is slightly more complicated. For example, say I want to find the probability of a die turning up a number that is a multiple of 2 or 3.
Then:
Probability of number that is multiple of 2 or 3 =
Probability of number that is multiple of 2
+ Probability of number that is multiple of 3
– Probability of number that is both a multiple of 2 and 3
Let’s check this the long way:
Out of 1, 2, 3, 4, 5 and 6, the numbers that are a
multiple of 2 or 3 are 2, 3, 4 and 6. This is 4 out of the 6 numbers which
works out to a probability of 
.
