Determine event independence using P(A and B)=P(A)P(B).
Find P(A and B) when events are independent
Problem
Given independent events with \(P(A)=1/4\) and \(P(B)=2/3\), calculate \(P(A\cap{}B)\) using the multiplication rule.
Big Picture
What this problem is really about
For independent events, the multiplication rule directly supplies their intersection probability. We’ll substitute the two marginals, multiply numerators and denominators, reduce the fraction, and check that the joint result does not exceed either individual probability.
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