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hernsl0263
08.12.2019 •
Mathematics
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?
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Ответ:
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) =
=![\frac{0.5}{0.6}](/tpl/images/0409/2167/96ea4.png)
P(X/Y) = 0.833
Ответ:
P(Favorable) = 0.6 and from this we have P(Successful) = 0.5 and P(unsuccesful) = 0.5
P(Unfavorable) = 0.4 and from this, we have P(Successful) = 0.3 and P(Unsuccesful) = 0.7
P(Successful) = (0.6×0.5) + (0.4×0.3) = 0.3 + 0.12 = 0.42
The question is a conditional probability: what is the probability of a program being successful GIVEN a program is favourable.
P(Successful | Favourable) = P(Successful∩Favourable) / P(Favourable)
P(S | F) = 0.42/0.6 = 0.7
Ответ:
the mistake was In marking of the decimal point and calculations in the answer he obtained
243.5475096 is the answer for the division