Statistics 101 · Worked example
Probability rules with worked examples
Probability measures how likely an event is, from 0 (impossible) to 1 (certain). Before choosing a formula, identify whether events overlap or whether one event changes the chance of another.
The method
Addition rule: P(A or B) = P(A) + P(B) − P(A and B). Conditional probability: P(B given A) = P(A and B) / P(A), when P(A) > 0. For independent events, P(A and B) = P(A) × P(B).
Worked example
Of 100 customers, 40 buy coffee, 30 buy tea and 10 buy both. Select one customer at random.
- P(coffee or tea) = 0.40 + 0.30 − 0.10 = 0.60.
- P(tea given coffee) = 0.10 / 0.40 = 0.25.
- Check independence: 0.40 × 0.30 = 0.12, which differs from the observed overlap of 0.10. These events are not independent.
Interpret the answer
A randomly selected customer has a 60% chance of buying coffee or tea. Among coffee buyers, 25% also buy tea.
A common mistake
Mutually exclusive events cannot happen together. Independent events do not change each other’s probabilities. These terms have different meanings.
Check your understanding
If two independent events have probabilities 0.5 and 0.2, what is the probability that both happen?
Show the answer
0.5 × 0.2 = 0.10, or 10%.
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