Question

A popular film series has produced 23 films of which 13 have been good. A new...

A popular film series has produced 23 films of which 13 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 13 out of 23. Historically, 67% of good films have a good trailer and 34.3% of bad films have a good trailer. The new film releases a good trailer. What is the probability that the film is good now?

IMPORTANT: 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.

Math   Statistics-And-Probability   
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Answer #1

Bayes' Theorem: P(A | B) = P(A & B)/P(B)

P(good film) = 13/23

P(bad film) = 1 - 13/23 = 10/23

P(good trailer | good film) = 0.67

P(good trailer | bad film) = 0.343

P(good film | good trailer) = P(good film and good trailer) / P(good trailer)

= P(good film and good trailer)/[P(good film and good trailer) + P(bad film and good trailer)]

= [(13/23)x0.67]/[(13/23)x0.67 + (10/23)x0.343]

= 0.71746

The required percentage= 71.746

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