Multiplication Rule for Independent Events

Multiplication Rule for Independent Events

When two events are independent, the outcome of one does not change the probability of the other. In that case, the probability that both happen is found by multiplying their probabilities.

1) Use the multiplication rule

For independent events A and B:

P(A and B) = P(A) × P(B)

If there are more than two independent events, multiply all their probabilities.

2) Substitute the given probabilities

Write each probability as a fraction, decimal, or percent as needed, then multiply carefully. Keep track of the event order if the problem names them separately, but for independent events the product is the same either way.

3) Simplify the result

Reduce fractions to lowest terms, or write decimals/percentages in the requested form. If the answer is a probability, it should usually be between 0 and 1.

4) Check your work

• Make sure the events are truly independent.
• Verify that each probability is valid.
• Confirm that the final value makes sense: multiplying probabilities should not increase the chance above either single event.

Quick example

If P(A) = 1/2 and P(B) = 3/4, then:

P(A and B) = 1/2 × 3/4 = 3/8

So the probability that both occur is 3/8.