I just need help with d) If persons A and B have a child, what’s the probability

Question

I just need help with d) If persons A and B have a child, what’s the probability of that child being affected? How is the answer 1/48???!!!!! Please explain all steps as it does not make sense to me. Thank you! 8. Consider the following pedigree of a rare autosomal recessive disease: a) parental genotypes? AA/aa b) F1 genotypes? Aa c) what are the phenotypic ratios of the F2 offspring? 100% not showing d) If persons A and B have a child, what is the probability of that child being affected? e) If persons A and B have 10 children, what is the probability of two children being affected? (101/218/) (1/48)2 * (47/48)8

Explanation / Answer

Lets see the genotypes of all the parents

I-1, i-4 should be AA as I-2 i-3 are aa (because none of their children is affected)

Now the parents in i-1 x i-2 and i-3 x i-4

ii-2, ii-3 and iii-4 will be Aa

As it is a rare disorder so let's consider ii-1, iii-1, iii-4 be AA (they are outside of the family)

For V-1 to be affected both iv-A and iv-B should be carrier.

And for A and B to be carrier iii-2 and iii-3 should be carrier.

Probability of iii-2 to be carrier =

AA x Aa

I.e 2/4

Probability of iii-3 to be the carrier =

Aa x Aa

As iii-3 is not shown to be affected so probability of it being the carrier is 2/3

For iv-A to be the varrier

AA x Aa

= 2/4(Aa)

Same goes for iv-B = 2/4

Probability of v-1 being affected

Aa x Aa

= 1/4 (aa)

To calculate overall probability of v-1 being affected let's multiply all the probabilities

2/4 * 2/3 * 2/4 * 2/4 * 1/4 = 1/48

A A a Aa Aa a Aa Aa

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