Question

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).41, (B).53, (C).67, (D).70, (E).83

Answer 1

(E) 0.83

Explanation:

We will solve it using conditional probability.

Let A be the event that a TV show is successful.

P(A) = 0.5

A' be event that the show is unsuccessful

P(A') =0.5

Let B be the event that the response was favorable

P(B) = 0.6

Let B' be the event that the response was unfavorable/

P(B') = 0.4

P(A∩B) = 0.5 and P(A∩B') = 0.3

We need to find new show will be successful if it receives a favorable response.

P(A/B) =
`(P(A∩B))/(P(B))`

= 0.5/0.6

= 0.833

Answer 2

Well, we know that in the past 60 % of the shows has favorable response and currently we have 50% network that receive the favorable response, the probability of the new show to receive favorable response would be :

50/60 = 0.83

Hope this helps