Determine event independence using P(A and B)=P(A)P(B).
Classify independence and mutual exclusivity with separate probability tests
Problem
For mutually exclusive events with \(P(A)=0.30\) and \(P(B)=0.40\), compare \(P(A\cap{}B)=0\) with \(P(A)P(B)\). Classify independence and mutual exclusivity separately.
Big Picture
What this problem is really about
Mutual exclusivity and independence require separate tests. We’ll use zero overlap to classify exclusivity, multiply the positive marginal probabilities for the independence benchmark, compare that nonzero product with the zero joint probability, and state both classifications without conflating them.
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