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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 :

WojtekR

Let's first denote:

F - a favorable response

F' - an unfavorable response

S - successful

We know that:

[tex]P(F) = 0.6\\\\P(F')=0.4\\\\P(F\cap S)=0.5\\\\P(F'\cap S)=0.3[/tex]

So, from the conditional probability, we can calculate:

[tex]P(S|F) = \dfrac{P(S\cap F)}{P(F)} = \dfrac{0.5}{0.6}=\dfrac{5}{6}\approx\boxed{0.83}[/tex]

Answer E.

Answer:

E IS CORRECT

Step-by-step explanation:

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