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.