Atelevision 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

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