Question

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?

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.

Answer 2

20% = 0.2

Explanation:

Let A = Wall Street Journal = 45%

Let B = USA Today = 40%

Let C = Both = 25%

C = A∩B = 25%

The focus is to determine that a random library subscribes to A only

The probability of subscribing to A = 45%

However, there are subscribers to A that are also subsribed to B

This group is C = 25%

To find the probability of subscribing to A only;

Probability of A only = P{A} - P{A∩B} = P{A} - P{C}

P{A} only = 45% - 25% = 20%

P{A} only = 0.2