Solving the Gender Probability of a Color-Blind Person

Suppose that 5 percent of men and 0.25 percent of women are color-blind. A color blind person is chosen at random. What is the probability of this person being male?

Color blindness is a condition that affects the way a person perceives color. The prevalence of color blindness varies between genders and ethnicities. In this article, we'll explore the probability of a randomly selected color-blind person being male.

Assumptions:

5% of men are color-blind.

0.25% of women are color-blind.

There are an equal number of males and females.

Calculations:

Let's call the probability of a randomly selected person being male "P(M)".

P(M) = 0.5 (Since there are equal number of males and females)

Next, let's calculate the probability of a randomly selected color-blind person being male, "P(CBM)".

P(CBM) = (Number of color-blind males / Total number of color-blind people)

P(CBM) = (0.05 * 0.5) / (0.05 * 0.5 + 0.0025 * 0.5)

P(CBM) = 0.9524

Finally, let's use Bayes' Theorem to find the probability of a color-blind person being male, given that a random person has been selected.

P(M/CB) = P(CB/M) * P(M) / P(CB)

P(CB) = P(CB/M) * P(M) + P(CB/F) * P(F)

P(CB) = 0.05 * 0.5 + 0.0025 * 0.5

P(M/CB) = 0.9524 * 0.5 / 0.0262

P(M/CB) = 71.43%

Based on our calculations, if a color-blind person is selected at random, the probability that they are male is 71.43%. It is worth noting that this result is based on the assumption of an equal number of males and females and the given prevalence of color blindness among males and females.