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

Answer:

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.

solved

general 11 months ago 1200