There are two prominent, nationally circulated newspapers, The Wall Street Journal and USA Today. Among all libraries across the country, 45

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?

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    2021-09-10T08:39:36+00:00

    Answer:

    20% = 0.2

    Step-by-step 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

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    2021-09-10T08:39:45+00:00

    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.

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