Hemophilia is a genetic disease that is caused by a recessive gene on the X chro

Question

Hemophilia is a genetic disease that is caused by a recessive gene on the X
chromosome.A woman is said to be a carrier of the disease if she has the hemophilia
gene on one X chromosome and the healthy gene on the other X chromosome. A
woman carrier has probability 1/2 of transmitting the disease to each son since a son
will get an X chromosome from the mother and a Y chromosome from the father.
Because of her family history a woman is thought to have a 50% chance of being a
carrier before having children. Given that this woman has three healthy sons, what
is the probability that she is a carrier?

Explanation / Answer

P(3 healthy sons) =P(have carrier and 3 health sons+not have carrier and 3 health sons)

=0.5*(1/2)3+0.5*1 =0.5625

hence P(she is a carrier| 3 healthy sons) =P(have carrier and 3 health sons)/P(healthy sons) =0.5*(1/2)3/0.5625

=0.1111

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