Hello!

What a wonderful question! It really shows that you are studying hard.

The reason for your confusion, as you correctly assumed, lies in the interpretation of the phrase "color blindness frequency"

Although I can see why you would think of this as the frequency of homozygous individuals,

let's try working through both interpretations.

1) Because males and females have different numbers of X chromosomes,

the q value must be calculated by dividing 2000 people into equal halves.

The number of affected individuals for females is given in the question, 160 people.

so if we assume that the question implied that "the number of affected individuals for males" is the same as females,

then we can get the exact same q^2 value for males = 160/1000 = 0.16

2) This q^2 value of 0.16 is essentially telling us 

"what are the chances of a male individual picking two X mutant chromosomes out of a box filled with either mutant or normal X chromosomes"

The problem is, males only have one X chromosome, so there is no need for us to calculate the probability for two Xs.

Because we are talking about probability, we only need to calculate the chance 

a male will pick "1 mutant X out of the box" not "2 mutant X out of the box".

Thus, we need to square root the 0.16, so we are only dealing with 1 mutant X,

giving us a q value of 0.4, which leads us to the correct answer choice.

3) You can raise your hand here and say, 

"what if affected male individuals already implies just picking 1 mutant X?"

In other words, the 0.16 value shouldn't be used as the q^2 value, but rather the q value.

Then your conclusion would be that for the male population q = 0.16, p = 0.84,

while in the female population q = 0.4, p = 0.6.

Here's where it gets tricky.

This conclusion is essentially saying that the allele frequency for colorblindness is different amongst the male and female populations.

This is a false conclusion.

Think of it like this: a colorblind son must inherit the Y chromosome from his father, and the mutant X chromosome from his mother.

In other words, the q allele inside the male is given from the female population, not the male population.

Likewise, the colorblind son can pass on his mutant X chromosome to his daughter.

So we cannot assume that X chromosomes for males and females are taken from separate boxes with different probabilities.

Everyone draws from the same box, and the chances of getting the mutant X is the same across all genders.

If you have different p and q values for two groups,

you are implying that these groups are separate from each other, and do not affect each others' allele frequencies.

But again, this cannot be the case, 

because the number of affected fathers is directly correlated with the grandmother's chances of having a mutant X 

as well as being directly correlated with his daughter's chances of receiving a mutant X.

4) You can argue that maybe there are different numbers of male individuals to begin with,

in other words, the actual q alleles can be passed back and forth between the genders, 

but still have different recessive allele "frequencies" because there are different numbers of males and females.

Which is why the problem states outright that the number of male and female individuals are equal.

Which ultimately leads us back to the question, what q value should we use for the male population.

The only logical conclusion is that both male and female populations share the same q value.

The problem gives us the q^2 value for females.

Thus, we should deduce the q value from the females and assume this to be true for males as well.

It is a difficult question, but a really good one, because it makes you think hard about what q and p values mean.

If you have additional questions feel free to ask. Hope this helps! :D