There are two prominent, nationally circulated newspapers, The Wall Street Journal and USA Today. Among all libraries across the country, 45% subscribe to The Wall Street Journal and 40% subscribe to USA Today, while only 25% subscribe to both The Wall Street Journal and USA Today. If a library is selected at random, what is the probability that it subscribes to The Wall Street Journal but not USA Today?

Question

Mathematics

Nolan Atkins

9 July, 08:18

There are two prominent, nationally circulated newspapers, The Wall Street Journal and USA Today. Among all libraries across the country, 45% subscribe to The Wall Street Journal and 40% subscribe to USA Today, while only 25% subscribe to both The Wall Street Journal and USA Today. If a library is selected at random, what is the probability that it subscribes to The Wall Street Journal but not USA Today?

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Answers (1)

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Adam · Answer 1

Let The Wall Street Journal be A, and USA Today be B. We want

P (A∩B^c), or the intersection of A and Not B happening.

P (A∩B^c) = P (A∪B) - P (B) = [P (A) + P (B) - P (A and B) ]-P (B)

= (0.45+0.40-0.25) - 0.40 = 0.2.