mammothrob
Junior Member
- Joined
- Nov 12, 2005
- Messages
- 91
Haemophilia is a sex-linked genetic disease that results in the inability of blood to clot. (A disease is sex-linked if the disease gene is located on X-chromosome.) A woman with one copy of the gene is a carrier, which means that she does not have the disease, but she can transmit it to her male children.
If a carrier has children by a man who is disease-free, each son has probability 0.5 of having the disease, and each daughter has probability 0.5 of being a carrier. Outcomes are independent.
a. A woman who is a carrier has two sons. The father is disease-free. What is the probability that neither of the sons has the disease?
b. A woman whose mother was a carrier has probability 0.5 of being a carrier. If this woman has a son by a man who is disease-free, what is the probability that the son has the disease?
c. Refer to part (b). If the son does not have the disease, what is the probability that the woman is a carrier?
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I will use ^ for intersection,
Im not sure if im looking at the problem the right way or not, but here goes.
I know that
the mom is a carrier and father is not disease free,
the probability of the son having the disease is P(S)=0.5 and P(S[sup:li9ts514]c[/sup:li9ts514])=0.5
the probability of the daughter having the disease is P(D)=0.5 and P(S[sup:li9ts514]c[/sup:li9ts514])=0.5
or P(S|W)=.5
a) P( S[sub:li9ts514]1[/sub:li9ts514] ^ S[sub:li9ts514]2[/sub:li9ts514]) = P(S[sub:li9ts514]1[/sub:li9ts514])P(S[sub:li9ts514]2[/sub:li9ts514]) = (.5)(.5)=.25
book says this answer is right, but I want to make sure I got it the right way.
b) So the mother is a carrier, her daughters probability of getting the disease is .5 ----- P(D|M) = .5
Now this daughter has a son with a man who is disease free, what is probability the son has the disease?
this is where i get mixed up on what to do.
P(S| P(D|M))=
or
P(S) ^ P(D|M) = (.5)(.5) = .25
book says .25 is right, but im sure if i got this correctly.
c) Probability that woman is a carrier if the son does not have disease?
P(W| S[sup:li9ts514]c[/sup:li9ts514])=
is this the right set up for this problem?
any feedback is much appreciated.
Rob
If a carrier has children by a man who is disease-free, each son has probability 0.5 of having the disease, and each daughter has probability 0.5 of being a carrier. Outcomes are independent.
a. A woman who is a carrier has two sons. The father is disease-free. What is the probability that neither of the sons has the disease?
b. A woman whose mother was a carrier has probability 0.5 of being a carrier. If this woman has a son by a man who is disease-free, what is the probability that the son has the disease?
c. Refer to part (b). If the son does not have the disease, what is the probability that the woman is a carrier?
-------------------------------------
I will use ^ for intersection,
Im not sure if im looking at the problem the right way or not, but here goes.
I know that
the mom is a carrier and father is not disease free,
the probability of the son having the disease is P(S)=0.5 and P(S[sup:li9ts514]c[/sup:li9ts514])=0.5
the probability of the daughter having the disease is P(D)=0.5 and P(S[sup:li9ts514]c[/sup:li9ts514])=0.5
or P(S|W)=.5
a) P( S[sub:li9ts514]1[/sub:li9ts514] ^ S[sub:li9ts514]2[/sub:li9ts514]) = P(S[sub:li9ts514]1[/sub:li9ts514])P(S[sub:li9ts514]2[/sub:li9ts514]) = (.5)(.5)=.25
book says this answer is right, but I want to make sure I got it the right way.
b) So the mother is a carrier, her daughters probability of getting the disease is .5 ----- P(D|M) = .5
Now this daughter has a son with a man who is disease free, what is probability the son has the disease?
this is where i get mixed up on what to do.
P(S| P(D|M))=
or
P(S) ^ P(D|M) = (.5)(.5) = .25
book says .25 is right, but im sure if i got this correctly.
c) Probability that woman is a carrier if the son does not have disease?
P(W| S[sup:li9ts514]c[/sup:li9ts514])=
is this the right set up for this problem?
any feedback is much appreciated.
Rob