Question 935071
following probabilities and conditional profitsfor ‘Claws’:
		

		PROFITS (Millions of $)

Level of success-------	Probability-------	Limited release-------		General distribution

Smash---------------------	.3--------------------- 22---------------------	12

Modest---------------------	.4--------------------- 9--------------------- 8

Bomb--------------------- .3	---------------------	    –10--------------	-------		  –2





If International Pictures' past experiences can be used as proxies for probabilities related to the current film "Claws," then let
P(S) = 0.3 be the probability that the film is a smash hit,
P(M) = 0.4 be the probability that the film is a modest success,
P(B) = 0.3 be the probability that the film is a total bomb,
P(E | S) = 0.90 be the probability of an excellent preview, given the film is a smash hit,
P(E | M) = 0.75 be the probability of an excellent preview, given the film is a modest success, and
P(E | B) = 0.40 be the probability of an excellent preview, given the film is a total bomb.

The posterior probability of a modest success given the sneak preview indicates excellent now can be written as
P(M | E) = P(M & E) / P(E)
= P(M)P(E | M) / [P(S)P(E | S) + P(M)P(E | M) + P(B)P(E | B)]
= (0.4)(0.75) / [(0.3)(0.9) + (0.4)(0.75) + (0.3)(0.4)]
= 0.30 / [0.27 + 0.30 + 0.12]
= 0.30 / 0.69
= 10 / 23
= 0.43 (to two decimal places).