Summary: p. 113, n. 60. There is a 50-50 chance the queen carries the gene for hemophilia. If she is a carrier, then
each prince has a 50-50 chance of having hemophilia. If the queen has had three princes without the disease,
what is the probability the queen is a carrier? If there is a fourth prince, what is the probability that he will
have hemophilia?
Solution. Let Qh be the event that the queen carries the gene for hemophilia and let Qn be the event that
she does not. Let Pi,h be the event that the i-th prince does not have hemophilia and let Pi,n be the event
that he does not. Then
P(Qh) =
1
2
, P(Pi,h|Qh) =
1
2
, P(Pi,h|Qn) = 0.
This implies that
P(Qn) = 1 - P(Qh) =
1
2
, P(Pi,n|Qh) = 1 - P(Pi,h|Qh) =
1

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics