People who are heterozygous (Aa) are carriers of an illness. A mother has 1/3 ch

Question

People who are heterozygous (Aa) are carriers of an illness. A mother has 1/3 chance of being a-allele (Aa) and her husband has 1/4 chance of being Aa. The couple is planning to have two children. What is the likelihood that both children will be healthy? Will the answer be as simple as 1/3*1/4*1/2*1/2 = 1/46 ?

Answer from expert:

No. Cross between Aa and Aa both will produce four genotypes - AA , 2Aa ,aa . Among them the first three that is 1 AA and 2 Aa will be healthy.And aa individual is going to have the illness. For this case the probability of healthy child of the couple is 3/4 that is among 4 types healthy types are 3. That is why the ans will be - chance of parents*chance of children = 1/3 * 1/4 * 3/4 = 3/48 = 1/16

- So then the probability of both kids being healthy is 1/3 * 1/4 * 3/4 * 3/4 = 9/192 = 0,046 = 4,6% ?

Explanation / Answer

Yes, the answer given by expert is correct.

As the probability of a child being healthy from the cross Aa x Aa is 3/4. So, if we combine all the probabilities then the chance of mother being a carrier is 1/3, chance of husband is 1/4 and each child have probability of 3/4.

So, 1/3*1/4*3/4*3/4 = 9/192.

That is 4.6 is the probability of both child being healthy.

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