Putting probability together
Probability measures how likely an event is to happen. It is always a number from 0 to 1. A probability of 0 means the event is impossible and a probability of 1 means it is certain. The list of all possible outcomes is the sample space.
Key idea
For equally likely outcomes, P(A) = (favourable outcomes) ÷ (total outcomes). The complement is P(A′) = 1 − P(A).
A step-by-step method
To solve a simple probability question, first find the total number of outcomes in the sample space. Next, count the outcomes that make the event happen. Then divide and simplify. If the question asks for "not", use the complement rule.
Worked example
A bag has 2 red, 3 green and 5 yellow balls of the same size. A ball is taken at random. Find (a) P(green) and (b) P(not green).
Total balls = 2 + 3 + 5 = 10.
(a) P(green) = 3 ÷ 10.
(b) P(not green) = 1 − 3/10 = 7 ÷ 10.
Sample space size
Listing the sample space helps you count correctly. For one fair die the sample space {1, 2, 3, 4, 5, 6} has 6 outcomes. For one coin, {Head, Tail} has 2 outcomes. Knowing this total is the key to every probability calculation.
Remember
- Probability is always between 0 and 1.
- Simplify fractions to their lowest terms.
- Use P(A′) = 1 − P(A) for "not" questions.