A physician-validated, board-style question from the Active Transport QBank. Try it, then check the reasoning for every option.
A healthy 29-year-old nulligravid woman comes to the physician for genetic counseling prior to conception. Her brother has a disease that has resulted in infertility, a right-sided heart, and frequent sinus and ear infections. No other family members are affected. The intended father has no history of this disease. The population prevalence of this disease is 1 in 40,000. Which of the following best represents the chance that this patient’s offspring will develop her brother's disease?
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A
0.7%Incorrect. 0.7% is too high; would correspond to misapplying the calculation (e.g., ignoring the patient's conditional probability or the father's carrier likelihood).
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B
1%Incorrect. 1% is the father's carrier probability alone — but you also need both parents to be carriers AND both to transmit the allele.
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C
66%Incorrect. 66% reflects only the patient's carrier probability (2/3) — doesn't account for the father's carrier probability or transmission.
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D
0.2%Correct. (2/3)(1/100)(1/4) = 1/600 ≈ 0.17% ≈ 0.2% — correct combined probability for offspring affected by autosomal recessive disease.
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E
0.05%Incorrect. 0.05% is too low — corresponds approximately to the population prevalence (1/40,000 ≈ 0.0025%) without accounting for the patient's elevated carrier probability (2/3) given her affected brother.
↑ Tap an answer to reveal the reasoning
Answer: D. The brother has Kartagener syndrome (primary ciliary dyskinesia): situs inversus (right-sided heart), recurrent sinusitis and otitis media (impaired mucociliary clearance), and infertility (immotile sperm flagella). PCD is autosomal RECESSIVE.
Using Hardy-Weinberg equilibrium, if disease prevalence (q²) is 1 in 40,000, then q = 1/200 ≈ 0.005 and 2pq (carrier frequency) ≈ 1/100 (population carrier rate).
The patient's brother is affected, so both parents must be carriers. The patient (unaffected sister) has a 2/3 probability of being a carrier (given she's unaffected, conditional probability among AA, Aa, aA, aa surviving as unaffected is 2 Aa out of 3 unaffected = 2/3).
The intended father has no family history; his probability of being a carrier equals the population carrier rate ≈ 1/100.
For an autosomal recessive child, both parents must be carriers AND both must pass the recessive allele. Probability = (2/3) × (1/100) × (1/4) = 2/1200 = 1/600 ≈ 0.0017 ≈ 0.2%.
This matches choice D.
**Why each option:**
**A.** 0.7% is too high; would correspond to misapplying the calculation (e.g., ignoring the patient's conditional probability or the father's carrier likelihood).
**B.** 1% is the father's carrier probability alone — but you also need both parents to be carriers AND both to transmit the allele.
**C.** 66% reflects only the patient's carrier probability (2/3) — doesn't account for the father's carrier probability or transmission.
**D.** (2/3)(1/100)(1/4) = 1/600 ≈ 0.17% ≈ 0.2% — correct combined probability for offspring affected by autosomal recessive disease.