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A television network is about to telecast a new television show. Before a show is launched, the network airs a pilot episode and receives a report assessing favorable or unfavorable viewer response. In the past, 60% of the network's shows have received a favorable response from viewers, and 40% have received an unfavorable response. If 50% of the network’s shows have received a favorable response and have been successful, and 30% of the network’s shows have received an unfavorable response and have been successful, what is the probability that this new show will be successful if it receives a favorable response? A.0.41 B.0.53 C.0.67 D.0.70 E.0.83

Respuesta :

nobillionaireNobley
Let P(F) represent the probability that the network's shows have received a favorable response from viewers and P(U) represent the probability that the network's shows have received an unfavorable response from viewers.

Then, P(F ∩ S) represents the probability that the network’s shows have received a favorable response and have been successful and P(U ∩ S) represents the probability that the network’s shows have received an unfavorable response and have been successful.


The probability that this new show will be successful if it receives a favorable response can be rephrased as the conditional probability that this new show will be successful given it receives a favorable response represented by P(S \ F)

From the given information,
P(F) = 60% = 0.6
P(U) = 40% = 0.4
P(F ∩ S) = 50% = 0.5
P(U ∩ S) = 30% = 0.3

[tex]P(S \backslash F)= \frac{P(S\cap F)}{P(F)} = \frac{0.5}{0.6} =0.83[/tex]

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