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A certain disease is found among a group of Native Indians. Children who inherit the disease will die by age of five. For the child to inherit the disease both parents have to carry the disease gene as a recessive trait. If both parents are carriers of the recessive gene the probability of the child's having the disease is $0.25$. Suppose a newly married indian couple are worried about having a child with this disease. They both tested for carrying the recessive gene and the test results are positive for one and negative for the other.

If the test that the couple took has a false positive rate of $0.01$ and a false negative rate of $0.02$ what is the probability that a child of theirs will have the disease?

What is the probability that when a child of theirs is tests positive that the test is actually a false positive (i.e. a test says that the child has the disease when it actually doesn't)?

Please explain clearly how to solve this problem preferably through a probability tree diagram or table. This is a sample problem for a test that I can't seem to understand, whatever I do.

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  • $\begingroup$ Have you tried creating the tree diagram ? $\endgroup$ – Shailesh Sep 14 '15 at 9:22
  • $\begingroup$ Yes, I know how to do it, and I know how to answer the first question with it. However, I don't know how to answer this question "What is the probability that when a child of theirs is tests positive that the test is actually a false positive (i.e. a test says that the child has the disease when it actually doesn't)?" with it. $\endgroup$ – trapdoors Sep 14 '15 at 9:26
  • $\begingroup$ Ok. I'll try to help. Give me some time unless someone else posts an answer in the mean time. $\endgroup$ – Shailesh Sep 14 '15 at 9:28
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    $\begingroup$ There's not enough information to answer the question. You need to know the prevalence of the disease or the frequency of the recessive gene. $\endgroup$ – joriki Sep 14 '15 at 9:48

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