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 <span>the network's shows have received an unfavorable response from viewers.
Then, P(F ∩ S) represents the probability that </span><span>the network’s shows have received a favorable response and have been successful and P(U ∩ S) represents the probability that </span><span>the network’s shows have received an unfavorable response and have been successful.
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The probability that this new show will be successful if it receives a favorable response can be rephrased as <span>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, </span>
P(F) = 60% = 0.6
P(U) = 40% = 0.4
<span>P(F ∩ S) = 50% = 0.5
</span><span>P(U ∩ S) = 30% = 0.3
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![P(S \backslash F)= \frac{P(S\cap F)}{P(F)} = \frac{0.5}{0.6} =0.83](https://tex.z-dn.net/?f=P%28S%20%5Cbackslash%20F%29%3D%20%5Cfrac%7BP%28S%5Ccap%20F%29%7D%7BP%28F%29%7D%20%3D%20%5Cfrac%7B0.5%7D%7B0.6%7D%20%3D0.83)
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