HELP Probability question for stats exam!!!!!!?

Question

Jessica is a film producer evaluation a new film proposal by Steven, a rookie screenwriter and director. Jessica knows that the probability of a film by new screenwriter being successful is only 20% with the probability if the film being a flop being 80%. We shall assume that a successful film will earn the studio a profit of $50 million and a flop will lose $20million. 1. Construct a decision tree for this problem. Should Jessica proceed with the film?
2.Compute expected value of perfect information for film decision.?
part 2:
Jessica would like to hire film critic, Feneva to read the script and asses the film s chances of success. Feneva predict a successful film 70% of the time & correctly predict unsuccessful film 80% of the time. 1. Construct a decision tree for the whole problem, including all probabilities
and payoffs. 2. Should Jessica hire Feneva?

Answer 1

1. It's kind of hard to draw the decision tree here. The film is successful with probability 0.20 and has a payout of 50. The film is a failure with probability 0.80 and has a payout of -20.

2. You find the expected value by multiplying each payout with its probability and then adding.

0.2*50 + 0.8*-20 = -6

Using this information, she should probably not proceed with the film.

1. We know the following probabilities.

P(Predict correct | successful) = 0.7
P(Predict correct | failure) = 0.8

We can split these as follows:

successful 0.2, predicted correct 0.7
successful 0.2, predicted incorrect 0.3
failure 0.8, predicted correct 0.8
failure 0.8, predicted incorrect 0.2

2. We can use Bayes' Rule to find the probability that Feneva is correct.

P(Correct) = P(successful)P(correct | successful) + P(failure)P(correct | failure)
= 0.2*0.7 + 0.8*0.8
= 0.78

So, yes, I would say that you should hire Feneva.