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.

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

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}}