A popular film series has produced 22 films of which 11 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 11 out of 22. Historically, 73.3% of good films have a good trailer and 22.6% of bad films have a good trailer. The new film releases a good trailer. What is the probability that the film is good now

76.43%

Step-by-step explanation:

Calculation for the probability that the film is good now

Let good film be :P(good film) = 11/22

Let bad film be : P(bad film) = 22-11/22 =11/22

P(good trailer | good film) = 0.733

P(good trailer | bad film) = 0.226

First step

P(good trailer)=11/22 (0.733)+11/22(0.226)

P(good trailer)=0.3665+0.113

P(good trailer)=0.4795

Second step

P(good film |good trailer )=0.733(11/22)/0.4795

P(good film |good trailer )=0.3665/0.4795

P(good film |good trailer )=0.7643*100

P(good film |good trailer )=76.43%

Therefore the probability that the film is good now will be 76.43%

a

step-by-step explanation: