Construct and interpret two-way frequency tables as sample spaces for independence and conditional probability.
Decide whether two events are independent from marginal and joint probabilities
Problem
Use joint probability to decide whether the variables are independent: \(P(A)=0.50\), \(P(B)=0.40\), \(P(A~\text{and}~B)=0.20\).
Big Picture
What this problem is really about
The joint form of the independence test compares the observed intersection with the product of the marginals. We’ll multiply the two given rates, place that expected joint beside the observed value, and classify the variables from exact equality rather than sums of probabilities.
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