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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?

1 Answer

4 votes

Answer: 0.57

This value is approximate and rounded to two decimal places

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

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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.

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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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