Construct and interpret two-way frequency tables as sample spaces for independence and conditional probability.
Interpret joint, marginal, and conditional probabilities from table counts
Problem
Interpret \(P(\text{senior}\cap{}\text{band})=12/80\) from the table. Identify its probability type and describe the numerator relative to \(\text{all}~80~\text{students}\).
An intersection with the grand total as denominator is a joint probability, not a conditional one. We’ll interpret both event conditions, locate their shared cell, identify the entire sample as the reference group, and express the fraction in words and percent form.
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