Multiplication Rule for Independent Events - Probability & Statistics Step by Step

For independent events A and B, use:

P(A∩B) = P(A) · P(B)

The outcome counts define each marginal probability separately.

Example

Multiply probabilities for independent events. Multiplying the probabilities is valid only under the assumption that the events are independent, which the book assumes rather than tests.

highlighted = computed this step

Step 1 — Probability of A

Compute the probability of event A.

P(A)= 3 / 6 = \hlmath{\frac{1}{2}}

Step 2 — Probability of B

Compute the probability of event B.

P(B)= 1 / 2 = \hlmath{\frac{1}{2}}

Step 3 — Multiply

Multiply independent probabilities.

P(A\cap B)= \frac{1}{2} \cdot \frac{1}{2} = \hlmath{\frac{1}{4}}

Step 4 — Result

State the joint probability.

P(A\cap B)= \hlmath{\frac{1}{4}}

multiplication-rule-independent P(A∩B) = P(A) · P(B)