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. 0.41 B. 0.53 C. 0.67 D. 0.70 E. 0.83

Answer 1

E IS CORRECT

Explanation:

Answer 2

Let's first denote:

F - a favorable response

F' - an unfavorable response

S - successful

We know that:

`P(F) = 0.6\\\\P(F')=0.4\\\\P(F\cap S)=0.5\\\\P(F'\cap S)=0.3`

So, from the conditional probability, we can calculate:

`P(S|F) = (P(S\cap F))/(P(F)) = (0.5)/(0.6)=(5)/(6)\approx\boxed{0.83}`

Answer E.