Chance a shopper buys fiction or non-fiction

Question

At a bookshop, 40\% of buyers purchase fiction, 35\% purchase non-fiction, and 15\% purchase both on the same visit. What is the probability that a randomly chosen buyer purchases at least one of the two kinds?

Accepted Answer

"At least one" means fiction or non-fiction or both. Adding 40\% and 35\% double counts the people who buy both, since they sit inside both groups. Inclusion-exclusion subtracts that shared slice once: P(	ext{fiction or non-fiction}) = 0.40 + 0.35 - 0.15 = 0.60. So 60\% buy at least one kind. Checking the four disjoint pieces: only fiction 0.25, only non-fiction 0.20, both 0.15, neither 0.40. They sum to 1.00, and the first three sum to 0.60. Takeaway. Add the two group sizes and remove the overlap once to avoid counting the people in both categories twice.

Chance a shopper buys fiction or non-fiction

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