Probability with numbers
Now that we know how to describe events with language, we will now investigate using numbers to calculate probabilities. If we can split up the sample space into equally likely outcomes and can identify the favourable outcomes making up an event, we can use the formula: \text{Probability} = \dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}
We can also use a useful fact about complementary events - since exactly one of them must happen, their probabilities always add to 1. This means if we know the probability of an event, the probability of the complementary event will be one minus the probability of the original: \text{Probability of complementary event} = 1 - \text{Probability of event}
Examples
Example 1
Consider this list of numbers: 2,\,2,\,2,\,3,\,3,\,3,\,4,\,4,\,5,\,5,\,5,\,7,\,7,\,7,\,7,\,9,\,9
A number is chosen from the list at random. What is the probability it is an odd number?
A number is chosen from the list at random. What number has the highest probability of being chosen?
Example 2
The probability of the local football team winning their grand final is 0.36.
What is the probability that they won't win the grand final?
If a sample space can be split up into equally likely outcomes, then we can use the following formula: \text{Probability} = \dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}
If two events are complementary then their probabilities will add to 1. This means: \text{Probability of complementary event} = 1 - \text{Probability of event}