Question
In: Statistics and Probability
Assume that you want to investigate the effects of TV commercials on a product. From the...
Assume that you want to investigate the effects of TV commercials on a product. From the questionnaire survey so far, we know the followings.
1. The probability that a purchaser of the product has watched the TV commercial is A.
2. The probability that a non-purchaser of the product has watched the TV commercial is B.
3. The probability that a customer buys the product is 0.1.
Let A = 0.6 and B = 0.2.
Question: What is the probability that a customer who has watched the TV commercial buys the product? ( Answer in the decimal form, not the fractional form.)
Solutions
Expert Solution
W : Event of watching the TV commercial
X : Event of Customer Buys the product
: Event of Customer does not buys the product
Probability that a purchaser of the product has watched the TV commercial : P(W|X) = A = 0.6
Probability that a non-purchaser of the product has watched the
TV commercial : P(W|)
= B =0.2
Probability that a customer buys the product : P(X) = 0.1
Probability that a customer does not buy the product :
P()
= 1-0.1 =0.9
Probability that a customer who has watched the TV commercial buys the product = P(X|W)
By Bayes Theorem,
Probability that a customer who has watched the TV commercial buys the product = 0.25
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