Question

a survey revealed that the probability that a person is entertained by reading books is 49%, the probability that a person is entertained by watching tv is 32%, and the probability that a person is entertained by both books and tv is 20%. what is the probability that a person will be entertained by books or tv (or both)?

a. 61
b. 20
c. 100
d. 81

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that a person is entertained by reading books (\(P(A) = 0.49\)) and \(B\) be the event that a person is entertained by watching TV (\(P(B)=0.32\)), and \(P(A\cap B) = 0.20\).

Step2: Substitute the values into the formula

Substitute \(P(A)=0.49\), \(P(B) = 0.32\), and \(P(A\cap B)=0.20\) into \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).

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Answer:

A. 61