Probability Of Crossover Gametes For Coupling Linkage

In coupling linkage, a crossover event occurs with a probability of 2p. When a crossover event occurs, we have 1/4AB, 1/4ab, 1/4Ab, and 1/4aB gametes.

Probability (crossover event) = 2p

When a crossover occurs we have

resulting gametes are 1/4 AB
resulting gametes are 1/4 aB
resulting gametes are 1/4 Ab
resulting gametes are 1/4 ab

This is because only 2 strands out of a total of 4 sister chromatids are involved in a crossover event.

Find the probability of a recombinant Ab gamete.

P(crossover event) x P[(aB gamete)/(given a crossover event)]
= 2p x 1/4 = 2p/4 = p/2

Find the probability of a recombinant aB type gamete.

P(crossover event) x P[(aB gamete)/(given a crossover event)]
= 2p x 1/4 = p/2

Probability of a crossover gamete = P(Ab) +P(aB)
Probability of a crossover gamete = p/2 + p/2 = p

Probability of a parental (non-crossover gamete)

1-probability(recombinant gamete) = 1 - p

We expect one-half of non-recombinant gametes to be AB and one-half to be ab types.

P(AB) = (1-p)/2
P(ab) = (1-p)/2

Probability(non-recombinant types) = (1-p)/2 + (1-p)/2 = 1-p