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October 6th, 2009, 10:09 PM   #1
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Basic Probability help

Ok, here's the problem.

The probability of a child inheriting a certain disease is 1/2. In a two child family, what is the probability that the younger child will inherit this disease given that the older child has already inherited it?

Here's what I've come up with, but I don't feel that it's right.

Events:
A=Older child is affected B=Younger child is affected
Looking for:
P(B|A)
Know:
P(A) = 1/2 P(B) = 1/2
Answer:
P(B?A)= (P(B?A))/(P(A))= (1/4)/(1/2)=2/4=1/2

I guess this makes sense because the probability of each child getting the disease is independent of the other one having the disease but a part of me feels that the answers should be 1/4
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October 7th, 2009, 02:49 AM   #2
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It does make sense, whereas 1/4 doesn't. However, the original wording "probability of a child inheriting a certain disease" is ambiguous; it could be interpreted as referring to "a particular child" or as referring to "at least one child".
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