Question

how do overlapping and non - overlapping events impact the calculation of probabilities?

Explanation:

For non - overlapping (mutually exclusive) events \(A\) and \(B\), the probability of \(A\) or \(B\) occurring is \(P(A\cup B)=P(A)+P(B)\) since there is no double - counting. For overlapping events \(A\) and \(B\), the probability of \(A\) or \(B\) occurring is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) to account for the overlap \(P(A\cap B)\) (the probability that both \(A\) and \(B\) occur simultaneously) which would otherwise be counted twice when simply adding \(P(A)\) and \(P(B)\).

Answer:

Non - overlapping events use \(P(A\cup B)=P(A)+P(B)\) and overlapping events use \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\) for probability calculation.