Let’s say that the probability that a randomly selected firm exports part of its

Question

Let’s say that the probability that a randomly selected firm exports part of its products knowing that it is a relatively large firm is equal to 60%. Also, let us assume that the simple probability that a randomly selected firm exports part of its products in equal to 20%, and that the simple probability that a randomly selected firm is fairly large is 15%. Compute the probability that a randomly selected firm is fairly large knowing that it exports part of its products.

*The answer is A, but I do not know how to show the work*

a) 45% -> Answer

b) 35%

c) 25%

d) 15%

e) We are going to need more information to compute this probability

Explanation / Answer

Ahh!, Simple problem , just apply conditonal probability formula:

given B, prob of A = P( A and B)/P(B)

P(exports | rel. large) = .6

P(export and rel.large)/ P(rel. large) = .6

P(exports) = .2

P(large) = .15

P(export and rel.large) = .6*15 = .09

P( large | exports) = ?

P(export and rel.large) /P(exports) = .09/.2

= .45

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