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nbme22/Block 2/Question#34

A 30-year-old man and a 24-year-old woman ...

1 in 600🔍

A 30-year-old man and a 24-year-old woman ...

1 in 600🔍

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*A questioner below asked, “Why is there a two-thirds probability of the father being a carrier?” Attaching my explanation via tangent to my original response* :)

We assume this is a recessive disease. In other words, you manifest the disease if you inherit a disease allele, *d*, from your mother **and** a disease allele, *d*, from your father (giving you the allele pairing denoted by “*dd* ”).

*dd* = you have the disease.

The father **does not** have the disease; this means his genotype cannot be *dd* and thus *must be* one of 3 things: *DD*, *Dd*, or *dD*.

That is,

*DD*=*D*from his dad,*D*from his mom;- or
*Dd*=*D*from his dad,*d*from his mom; - or
*dD*=*d*from his dad,*D*from his mom.

Notice that in only two of these 3 possibilities (⅔) does the father (potentially) have a disease allele, *d*, that he might pass on to his progeny.

Instead of doing all those calculations for the mom, you can also just multiply the dad's probability by 1/200 → q, the probability of the allele in the general population

Mandelian Genetics:

Man has **2/3** chance of being a carrier. (He does not have the disease).
Woman carrier risk must be calculated with p^2 + 2pq + q^2.
q^2 = 1/40,000
q = 1/200, p is roughly = 1
2pq = 1/100 = Carrier frequency .

Risk of having a child thus equals **2/3 x 1/100 x 1/4 = 1/600**
Because:
2/3 = Man Carrier risk
1/100 = Female Carrier Risk
1/4 = Chance they each pass on the recessive gene to their offspring.

The probability of the father being a carrier is 2/3 since it is known that he doesn’t have the disease. Then the probability of him passing it on to his kid is:

`1/2 * 2/3 = 1/3`

With the Hardy-Weinberg Principle, you can figure out the probability of the mother being a carrier:

`q = sqrt(1/40,000) = 1/200`

So, `2pq = 2 * 1/200 * 199/200`

, which approx is 1/100, and the probability of the child getting this allele is `1/100 * 1/2 = 1/200`

Thus:

`1/200 * 1/3 = 1/600`

brill45
You did this right but I think made it a bit more complicated than needed to be. To figure out the likelihood of a random person in the population passing on a recessive allele, you just need to do squareroot(q2) to get to q. And just use that q to multiply with the 1/3 you got earlier. The q value tells you the allele frequency in the population, whether the person is a carrier or homozygous recessive both. You still got it, but just letting you know the easier route in case you see it again!
+2

This the same as @keycompany's explanation with more explanation those that need it...

The patient is unaffected by the particular autosomal recessive disease and his brother has the autosomal recessive disease --> this means each of their parents carries the AR allele. Now, for the patient to be *unaffected* given that both his parents have the AR allele, it means that the patient has a 2/3 chance that he is simultaneously unaffected *and* a carrier.

The patient's partner is unaffected and normal Hardy-Weinberg genetics (as stated in the problem)..when this is specifically mentioned, you are to assume that the partner has a carrier frequency for the AR allele, which equal to 2pq.

The disease has a frequency in the population of 1/40000. This is q^2 --> q^2 = 1/40000. Solving for q, you get q = 1/200.

Carrier frequency is 2pq. **However**, for a ** rare** disease, 2pq ≈ 2q. So, the carrier frequency for the partner = 2q = 2 * 1/200 = 1/100.

Now, the Q asks about an offspring of the patient and his partner being *affected*, so to have an affected child, there is a 1/4 chance of having an affected child (becasuse the patient and the partner both have a 1/2 chance of passing the allele --> you multiple these together 1/2 * 1/2).

**So, multiply 2/3 * 1/100 * 1/4 = 1/600. This is P(patient being a carrier) * P(partner being a carrier) * P(having an affected offspring together).**

why there is probability of father being a carrier is 2/3

drdoom
We assume this is a recessive disease. In other words, you manifest the disease if you inherit a disease allele, d, from your mother and a disease allele, d, from your father, giving you an allele pairing denoted by dd. dd = you have the disease. The father does not have the disease; this means his genotype can only be 1 of three things: DD, Dd, or dD. That is, DD = D from his dad, D from his mom; Dd = D from his dad, d from his mom; or dD = d from his dad, D from his mom. Notice that in only two of these 3 possibilities does the father (potentially) have a disease allele (d) that he might pass on to his progeny.
+

We assume this is a recessive disease. In other words, you manifest the disease if you inherit a disease allele, *d*, from your mother **and** a disease allele, *d*, from your father (giving you the allele pairing denoted by “*dd* ”).

*dd* = you have the disease.

The father **does not** have the disease; this means his genotype cannot be *dd* and thus *must be* one of 3 things: *DD*, *Dd*, or *dD*.

That is,

*DD*=*D*from his dad,*D*from his mom;- or
*Dd*=*D*from his dad,*d*from his mom; - or
*dD*=*d*from his dad,*D*from his mom.

Notice that in only two of these 3 possibilities (⅔) does the father (potentially) have a disease allele, *d*, that he might pass on to his progeny.

submitted by drdoom(460), 2019-05-31T12:16:37Z

Calculations for dad. The probability of the father being a carrier is 2/3 since it isknownthat he doesn’t have the disease. Then the probability of him passing it on to his kid is 1/2, thus:Calculations for mom. With the Hardy-Weinberg Principle, you can figure out the probability of the mother being a carrier:`q = sqrt(1/40,000) = 1/200`

So,

`2pq = 2 * 1/200 * 199/200`

, which is approx 1/100.For the child to get the allele from mom, two things need to happen: (1) mom must be a carrier [“heterozygote”] and (2) mom must pass the allele to child:

Puting it all together. Now, combine all together:= (probability of dad being carrier) * (probability of dad passing on disease allele) * (probability of mom being carrier) * (probability of mom passing on disease allele)

=

`2/3 * 1/2 * 1/100 * 1/2`

=

`1 in 600`