Question asks the probabily of offspring from individuals 4 and 7 to be affected

Question

Question asks the probabily of offspring from individuals 4 and 7 to be affected.

Answer apprently is 1/3, but I don't understand why.

Here is my flow of reasoning.

1. Clearly the trait is recessive.

2. Since #2 is affected (aa) while neither of his parents are, both parents must be Aa.

3. For individual #7, mother is affected (aa) and her sister is also affected (aa). This tells us that the father (who is unaffected) must be Aa since crossing between aa with AA would not be possible to yield affected offspring like #6. This means that Individual #7 (who is unaffected), must be Aa since crossing between aa and Aa cannot yield AA offspring.

4. OK, so we know that #4 is unaffected offspring from ( Aa x Aa). And from Aa xAa, it is 1/3 likely that offspring is AA and 2/3 to be Aa. For individual #7, we know for sure she is Aa.

5. Offspring from #4 and #7 must be aa for him to be affected. which is only possible if #4 is Aa.

6. Hence... (2/3) x (1) x ( 1/4) = 1/6. which means prob. of #4 being Aa x p of #7 being Aa x p of offspring being aa from this.

so why is this wrong?

Explanation / Answer

1. the condition is autosomal recessive.

2. the individual 4 will be AA or Aa, their parents are Aa*Aa, so the probability of the offspring not affected comes out to be 2/3 Aa and 1/3 AA while 1 is affected aa. so the offspring 4 will be either AA or Aa.

3. the individual 7 is unaffected and is Aa for sure as the mother is affected and is aa but the father is unaffected and is Aa. this is because if a father is AA then there will not be any affected child so the father is Aa and mother is aa. so the individual 7 is Aa and the probability of Aa is 1/2.

So now the offspring from 4 and 7 to carry the trait the parents need to carry the recessive trait. if the parent is AA and Aa then the offspring will not be affected. so the offspring to be affected the parents should be Aa and Aa. so now the probability of the offspring to be affected will come out to be 2/3 * 1/2, which is probability of 4 being Aa and probability of 7 being Aa. so this comes out to be 1/3 for the offspring to be affected.

hope it is clear now.

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