Understand conditional probability and connect independence to unchanged conditional probabilities.
Decide whether two events are independent by comparing a probability to its conditional probability
Problem
Use conditional probability to decide whether the events are independent: \(P(A)=0.40\) and \(P(A|B)=0.40\).
Big Picture
What this problem is really about
With a positive conditioning probability, independence means conditioning on B leaves A’s probability unchanged. We’ll state that criterion, compare the conditional value with A’s marginal value, interpret equality as no probability shift, and classify the events without comparing to the wrong marginal.
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