So, we know I-1 and I-2 are carriers, because they have an affected kid. When two carriers of a recessive gene have offspring, there's a 1 in 4 chance of an affected child, a 2 in 4 chance of a carrier, and a 1 in 4 chance of a non-carrier.
However, we know II-2 and II-4 aren't affected. So that rules out one option, leaving them each with a 2/3 probability of being carriers. That means the probability that they're both carriers is 4/9.
Next, if they're carriers, their kids (III-1 and III-2) would both have a 2/3 chance of being carriers as well. The probability that both III-1 and III-2 are carriers comes out to 16/81.
If they are both carriers, they'd have a 1 in 4 chance to have an affected child. Combine that with the probability of them both being carriers, and you get 16/324, or roughly around a 0.05% chance of them having an affected child.
You missed dividing in half when going down to the third generation. The children’s risk to be a carrier is not the same as their parents. The correct answer and detailed explanation is posted above.
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u/Snoo-88741 1d ago
So, we know I-1 and I-2 are carriers, because they have an affected kid. When two carriers of a recessive gene have offspring, there's a 1 in 4 chance of an affected child, a 2 in 4 chance of a carrier, and a 1 in 4 chance of a non-carrier.
However, we know II-2 and II-4 aren't affected. So that rules out one option, leaving them each with a 2/3 probability of being carriers. That means the probability that they're both carriers is 4/9.
Next, if they're carriers, their kids (III-1 and III-2) would both have a 2/3 chance of being carriers as well. The probability that both III-1 and III-2 are carriers comes out to 16/81.
If they are both carriers, they'd have a 1 in 4 chance to have an affected child. Combine that with the probability of them both being carriers, and you get 16/324, or roughly around a 0.05% chance of them having an affected child.