Below is a pedigree from a family that lives in a population (in equilibrium) where the frequency of an autosomal recessive genetic allele is 1 in 150 . II-1 is affected by this recessive disease. What is the probability that the child (III-1) will have this disease? (Pick the closest value.)

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∻Answer∻ ⚹ 1/600 ⚹ ∻Solution∻ ‖ a ⋮ Calculate the allele frequency (q) for the recessive allele: Given the frequency of the recessive allele is 1 in 150, we denote this as $q$. Since the population is at equilibrium, we can use the Hardy-Weinberg principle to find the frequency of the homozygous recessive genotype ($q^2$). ‖ ‖ b ⋮ Determine the frequency of the homozygous recessive genotype ($q^2$): Using the allele frequency $q = \frac{1}{150}$, we calculate $q^2 = \left(\frac{1}{150} ight)^2$. ‖ ‖ c ⋮ Calculate the frequency of the carriers (heterozygous genotype, $2pq$): The frequency of the dominant allele (p) is $p = 1 - q$. The carrier frequency is $2pq = 2 imes (1 - q) imes q$. ‖ ‖ d ⋮ Determine the probability that both parents of III-1 are carriers: Since II-1 is affected, both parents of II-1 must be carriers. The probability that III-1's parent (II-2) is a carrier is $2pq$. ‖ ‖ e ⋮ Calculate the probability that III-1 will inherit the disease: The child III-1 will be affected only if they inherit the recessive allele from both parents. The probability is $\frac{1}{4}$ if both parents are carriers. ‖ ‖ f ⋮ Combine the probabilities: The probability that III-1 will have the disease is the probability that II-2 is a carrier ($2pq$) times the probability that III-1 inherits the disease from carrier parents ($\frac{1}{4}$), which is $2pq imes \frac{1}{4}$. ‖ ∻Key Concept∻ ⚹ Hardy-Weinberg equilibrium and autosomal recessive inheritance ⚹ ∻Explanation∻ ⚹ The Hardy-Weinberg principle allows us to calculate allele frequencies and predict genotype frequencies in a population at equilibrium. For an autosomal recessive disease, the probability that a child will inherit the disease depends on the parents' genotypes and the inheritance of alleles. ⚹◊What is the formula for calculating the probability of inheriting an autosomal recessive genetic disease in a pedigree?⍭ Generate me a similar question◊

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