Question

In a certain population of rats, brown fur coloring is dominant to gray. if you have 112 brown rats in a population of 200 rats (with the rest of them being gray), what is the predicted frequency of homozygous dominant rats?

A. 0.11
B. 0.45
C. 0.54
D. 0.15

Answer 1

Option A

Step-by-step explanation:

Given -

Total population of rats
`= 200`

Out of the total population, number of rats with brown fur
`= 112`

Thus , the frequency of brown fur rats

`= (112)/(200) \\= 0.56`

It is also given that the brown fur rats are dominant to gray fur rats.

As per Hardy Weinberg's equation,

Frequency of dominant rats is given by
`p^2`

and here

`p^2 + 2pq = 0.56`

Thus,

Frequency of homozygous recessive gray rat

`p^2 + q^2+2pq = 1\\\\q^ 2 = 1-0.56\\ q^ 2 = 0.44\\q = 0.663`

Hence,

`p = 1-q\\= 1-.663\\\\= 0.337\\`

frequency of homozygous dominant rats

`= p^2\\= 0.337^2\\= 0.1135`

Hence, option A is correct