In a recent study, 0.72 were smokers and were 0.41 male smokers. What is the probability that if the person surveyed is a smoker then he is a male?

This value is approximate and rounded to two decimal places

The more accurate value is roughly 0.569444444 where the 4's repeat forever.

Work Shown:

M = person is a male

S = person is a smoker

P(S) = 0.72

P(M and S) = 0.41

P(M given S) = P(M and S)/P(S) conditional probability

P(M given S) = 0.41/0.72

P(M given S) = 0.5694444 approximately

P(M given S) = 0.57

I'm rounding to two decimal places because the other given values 0.72 and 0.41 are also to two decimal places.

Here's another way to think about it.

Let's say there are 100 people surveyed. If 72 are smokers, then P(S) = 72/100 = 0.72

If out of those 100 people, 41 are male smokers then P(M and S) = 41/100 = 0.41

We're asked to find the probability of picking someone who is male given we know they are a smoker. So we just focus on the 72 smokers ignoring the 28 other nonsmokers. Of those 72 people, 41 are male, so 41/72 = 0.569444 = 0.57 approximately.

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