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1 in 100 men and 1 in 300 women have some type of red-green colorblindness. Assuming the population is 50% men and 50% women, what is the average rate of red-green colorblindness?

I assume that because it’s 50/50, I would simply take the arithmetic mean?

$$\frac{\frac{1}{100} + \frac{1}{300}}{2} = 1/150 \approx 0.66\%$$

Or do I add each part?

$$\frac{1}{100} \& \frac{1}{300} = \frac{2}{400} = 0.5\%$$

What would happen if it weren’t 50/50, for example, 40/60?

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  • $\begingroup$ Do you know the law of total probability? $\endgroup$
    – Zhanxiong
    Commented Oct 20, 2017 at 2:28
  • $\begingroup$ Try imagining there are 1200 people. Then think about it when the population is split 50/50 or any other mix (try 75/25). You can generalize from there. $\endgroup$
    – eSurfsnake
    Commented Oct 20, 2017 at 2:38

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p(male)*p(cb|male) + p(female)*p(cb|female)

So your first option needs to be modified to account for probability of being male or female, if you have unequal distribution.

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