The probability of having exactly three normal children among five, when both parents are heterozygous carriers for the autosomal recessive cystic fibrosis allele, is 0.26.

Genetic Basis

Cystic fibrosis follows autosomal recessive inheritance, requiring two recessive alleles (ff) for the disease to manifest. Heterozygous parents (Ff × Ff) produce offspring with genotypes FF (25%, normal non-carrier), Ff (50%, normal carrier), or ff (25%, affected). Thus, the probability of a normal child (FF or Ff) per birth is p = 0.75 (3/4).

Binomial Probability Setup

This scenario fits the binomial distribution, modeling n = 5 independent trials (children) with success probability p = 0.75 for normal phenotype and exactly k = 3 successes. The formula is:

P(k) = (n k) pk (1-p)n-k, where (5 3) = 10 and 1-p = 0.25.

Step-by-Step Calculation

Compute (5 3) × (0.75)3 × (0.25)2 = 10 × 0.421875 × 0.0625 = 0.263671875, rounded to 0.26. Punnett square confirms single-child ratios; binomial extends to multiple offspring.

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Unlock Probability of Exactly Three Normal Children Among Five in Cystic Fibrosis Cases

In probability of exactly three normal children among five cystic fibrosis heterozygous parents, autosomal recessive inheritance patterns are key for CSIR NET aspirants. Both parents as carriers (Ff) yield 75% normal offspring per child, making binomial probability essential for exam success.

Autosomal Recessive Inheritance Explained

Cystic fibrosis requires homozygous recessive (ff) genotype. Heterozygous parents produce:

  • 25% FF (normal)
  • 50% Ff (carrier, normal)
  • 25% ff (affected)

Normal child probability: 0.75. Punnett square visualizes this 3:1 normal-to-affected ratio.

Binomial Distribution Application

For five children, exactly three normal uses P(3) = (5 3) (0.75)3 (0.25)2:

  • (5 3) = 10
  • (0.75)3 = 0.421875
  • (0.25)2 = 0.0625
  • Total: 0.26 (two decimal places)

This matches CSIR NET quantitative genetics problems.

CSIR NET Exam Insights

No options provided, but direct computation yields 0.26. Common distractors: at-least-three (higher), any-three-affected (low). Master via practice for molecular biology sections.