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

The closest answer I have found for this to be correct is 0.54 I divided 112 and 200 and got 0.56

Answer 2

Answer:

Option A

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

$= \frac{112}{200} \\= 0.56$

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