A popular film series has produced 20 films of which 9 have been good. A new fil

Question

A popular film series has produced 20 films of which 9 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 9 out of 20. However, 62.48% of films with a good trailer turn out to be good while 35.42% of bad films have a good trailer. The new film releases a good trailer. What are the odds that the film is good now?

Put your answer in percentage form (e.g. 10.71 not 0.1071) and then round to two decimal places. Do not include a % sign.

Explanation / Answer

Ans:

P(good film)=9/20

P(bad film)=11/20

P(good trailer/good film)=0.6248

P(good trailer/bad film)=0.3542

P(good trailer)=0.6248*(9/20)+0.3542*(11/20)=0.4760

Now,

P(good film/good trailer)=P(good trailer/good film)*P(good film)/P(good trailer)

=0.6248*(9/20)/0.4760

=0.5907 or 59.07%

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