Multiplication Rule (Independent)
Probability of both independent events occurring.
Formula
Variables
Example
Two heads: 0.5 × 0.5 = 0.25
How it works
When two events are independent, the outcome of one does not change the chance of the other. That means the probability that both happen is found by multiplying their separate probabilities, because each event contributes its own chance without affecting the other. This rule comes from counting all possible combined outcomes in a situation where the events do not influence each other.
When to use it
Use this formula when one event has no effect on the probability of the other, such as repeated fair coin flips, independent machine failures, or separate random draws with replacement. It is especially useful in basic probability problems involving "and" statements for independent events.
Worked example, step by step
A spinner lands on red with probability 0.2, and a fair die shows a 6 with probability 1/6. These events are independent, so multiply the probabilities. P(red and 6) = P(red) × P(6) P(red and 6) = 0.2 × 1/6 P(red and 6) = 0.2 × 0.1667 P(red and 6) ≈ 0.0333 Final answer: 0.0333, or about 3.33%
Common mistakes to avoid
- Adding the probabilities instead of multiplying them
- Using this rule when the events are not independent
- Forgetting to convert a percentage or fraction into a probability before multiplying
Did You Know?
Independence means one event does not affect the other.
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