Question

Assume that in a one locus, two-allele system (alleles A and a), the frequency of the A

allele is p and the population is in Hardy-Weinberg equilibrium. Now, assume we catch

a single random female, randomly collect two eggs from her, and determine the genotype

of each of these eggs. What is the probability that in this experiment we will get two eggs

carrying the A allele? Express the answer in terms of p.

Answer 1

Solution:-

1. Eggs are nothing but offspring of bird
2. If frequency of A is p and frequency of 'a' is q, and p+q = 1 (Hardy Weinberg)
Now if we square both sides - p² + q² +2pq = 1

The probability of egg carrying A is in two cases - either homozygous A or heterozygous Aa, these two cases are mathematically - p² + 2pq

Probability = favorable outcomes / total outcomes

Probability = (p² +2pq) / 1 - This is 1st equation

Now, p+q = 1 (Hardy Weinberg)
So, q = 1 - p (Substitute in 1st equation)

p² + 2p(1-p) = probability
p² + 2p -2p² = 2p -p² = p(2-p) = probability

Thus probability = p(2-p)

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