Question
In: Statistics and Probability
A popular film series has produced 24 films of which 16 have been good. A new...
A popular film series has produced 24 films of which 16 have been good. A new film from the series is about to come out, and without any additional information we would assume that the odds it is good is 16 out of 24. Historically, 65.7% of good films have a good trailer and 21.8% of bad films have a good trailer. The new film releases a good trailer. What is the probability that the film is good now?
put your answer in percentage form (e.g. 72.4218 not 0.724218) and then round to four decimal places. You do NOT need to include a % sign.
Solutions
Expert Solution
Result:
A popular film series has produced 24 films of which 16 have been good. A new film from the series is about to come out, and without any additional information we would assume that the odds it is good is 16 out of 24. Historically, 65.7% of good films have a good trailer and 21.8% of bad films have a good trailer. The new film releases a good trailer. What is the probability that the film is good now?
put your answer in percentage form (e.g. 72.4218 not 0.724218) and then round to four decimal places. You do NOT need to include a % sign.
let
GF= Good film BF= Bad film GT= Good trailer
Given:
P(GF) = 16/24 P( BF) = 8/24
P(GT/GF) =0.657 P( GT/BF) = 0.218
We know that from Bayes Theorem, P( GT) = P(GF)* P(GT/GF)+ P(BF)* P(GT/BF)
=(16/24)*0.657+(8/24)*0.218
=0.510667
P( GF/GT) = P(GF)* P(GT/GF)/P( GT)
=(16/24)*0.657/0.510667
=0.857702
The required percentage= 85.7702
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