probability bayes theorem

I would ask some more questions.Thanks a lot again.
So,
there are 10,000 people in total, it is the population.
there's a table


male female
smoker 15% 20%
not smoker 35% 30%

It says, knowing that a person is taken randomly from the population and that this person smokes, compute the probability that it is a woman.

The book says

P(F|S) proportional(I do not know how to write that kind of infinite symbol) to P(F) P(S|F) = 0.5 x 0.4
P(M|S) proportional to P(M) P(S|M)= 0.5x 0.3

why does it write o.4 and 0.3? should not it be respectively 0.20 and 0.15? thanks a lot for your help!

Quote:

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Originally Posted by 0123

I would ask some more questions.Thanks a lot again.
So,
there are 10,000 people in total, it is the population.
there's a table


male female
smoker 15% 20%
not smoker 35% 30%

It says, knowing that a person is taken randomly from the population and that this person smokes, compute the probability that it is a woman.

The book says

P(F|S) proportional(I do not know how to write that kind of infinite symbol) to P(F) P(S|F) = 0.5 x 0.4
P(M|S) proportional to P(M) P(S|M)= 0.5x 0.3

why does it write o.4 and 0.3? should not it be respectively 0.20 and 0.15? thanks a lot for your help!

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10000 people, 1500 are male smokers, 2000 are femail smokers,
3500 are male nonsmokers and 3000 are femail non-smokers.

random individual is a smoker means that we have a ranom individual
form the 3500 smokers so the probability that it is a woman is

p=2000/3500

Or P(F|S)P(S)=P(S|F)P(F) by Bayes theorem.

RonL