SOLUTION: 60% of the patients at a clinic are children. 10% of the children and 1/4 of the adults use alternative medicine. A patient is selected at random. 1) what is the probability t

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Question 189206: 60% of the patients at a clinic are children. 10% of the children and 1/4 of the adults use alternative medicine. A patient is selected at random. 1) what is the probability the slected patient uses alternative medicine? 2) what is the probability that the selected patient is a child that uses alternative medicine?
Answer by stanbon(75887) About Me  (Show Source):
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60% of the patients at a clinic are children. 10% of the children and 1/4 of the adults use alternative medicine. A patient is selected at random. 1) what is the probability the slected patient uses alternative medicine? 2) what is the probability that the selected patient is a child that uses alternative medicine?
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P(C) = 0.60 ; P(C') = 0.40 ;
P(A|C) = 0.10 ; P(A'|C) = 0.9;
P(A|C') = 0.25 ; P(A'|C') = 0.75
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Question # 1:
P(A) = P(A and C) + P(A and C')
= P(A|C)P(C) + P(A|C')P(C')
Substitute from above to get answer = 0.1006
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Question # 2
P(C and A) = P(A|C)P(C) = 0.10*0.60 = 0.0006
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Cheers,
Stan H.