By birth there is a 50{50 chance that the queen carries the gene for hemophilia.
ID: 3319098 • Letter: B
Question
By birth there is a 50{50 chance that the queen carries the gene for hemophilia. If she is a carrier, then each prince has a 50{50 chance of having hemophilia. If she is not a carrier, the chance of a prince having hemophilia is almost zero.
1. Suppose the queen has given birth to one prince. If we nd out that the prince does not have the disease, then what is the probability that the queen is a carrier given the
new piece of information?
2. Suppose the queen has given birth to two princes, both without the disease. What is the probability that the next prince has the disease?
(Hint: Bayesian.]
Explanation / Answer
1) probability that prince does not have the disease =P(Queen has disease and price does not have +Queen does not have disease and price does not have)=0.5*0.5+0.5*1=0.75
therefore probability that the queen is a carrier given prince does not have the disease
=P(Queen has disease and price does not have)/P(prince does not have the disease)
=0.5*0.5/0.75=1/3
2)probability that both prince do not have the disease =P(Queen has disease and price do not have +Queen does not have disease and price do not have)=0.5*0.5*0.5+0.5*1*1=0.625
hence P(Queen has disease)=P(Queen has disease and price do not have)/P(both prince do not have the disease)
=0.5*0.5*0.5/0.625=1/5=0.2
hence probability that the next prince has the disease=P(queen has disease) and next price has disease
=0.2*0.5 =0.1
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