SOLUTION: the probability is 0.6 that a person selected at random from the current residents of a certain hospital will be a male . the probability that the patient will be a male who is in

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Question 1084186: the probability is 0.6 that a person selected at random from the current residents of a certain hospital will be a male . the probability that the patient will be a male who is in for surgery is 0.2 A patient randomly selected from the current residents is found to be a male ,what is the probability that he is in the hospital for surgery ?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

M = patient is male
S = patient is in for surgery
M and S = patient is male AND in for surgery

Given info:
P(M) = 0.6
P(M and S) = 0.2

Using that info, we can compute the conditional probability
P(S|M) = [P(M and S)]/P(M)
P(S|M) = 0.2/0.6
P(S|M) = 2/6
P(S|M) = 1/3
P(S|M) = 0.33333 (this is approximate)
P(S|M) = 33.333% (this is approximate)

There is roughly a 33.333% chance he is in for surgery given this patient is male.