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?

The probability that this new show will be successful if it receives a favorable response is 0.833

Step-by-step explanation:

We are going to solve this problem using conditional probability. From the question lets state some of the conditions.

Let X be the event that the TV show is successful, so the probability that the TV show is successful is P(X) = 0.5

Let X' be the event that the TV show is unsuccessful, so the probability that the TV show is unsuccessful is P(X') = 0.5

Let Y be the event that there was a favorable response, so the probability that the show had a favorable response P(Y) = 0.6

Let Y' be the event that there was an  unfavorable response, so the probability that the show had an unfavorable response P(Y') = 0.4

If 50% of the network’s shows have received a favorable response and have been successful then,

P(X∩Y) = 0.5

and 30% of the network’s shows have received an unfavorable response and have been successful then,

P(X∩Y') = 0.3

The probability that this new show will be successful if it receives a favorable response will be

P(X/Y) = =

P(X/Y) = 0.833

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step-by-step explanation:

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