Question

Color Blindness The most common form of color blindness is red–green color blindness. People with this type of color blindness cannot distinguish between green and red. Approximately 8% of all males have red–green color blindness, while only about 0.64% of women have red–green color blindness. In 2000, 49.1% of all Americans were male and 50.9% were female according to the U.S. Census Bureau

. (a) What is the probability that a randomly selected American is color blind?

b) What is the probability that a randomly selected American who is color blind is female?

Answer 1

We are given here that:
P( male ) = 0.491,
P( females ) = 0.509

Also, we are given here that:
P( color blind | male ) = 0.08
P( color blind | female ) = 0.0064

a) Using law of total probability, we get here:
P( color blind ) = P( color blind | male ) P(male) + P( color blind | female )P(female )

P( color blind ) = 0.08*0.491 + 0.0064*0.509 = 0.0425376

Therefore 0.0425376 is the required probability here.

b) Given that the person is color blind, probability that the person is female is computed using Bayes theorem here as:

P( female | color blind) =  P( color blind | female )P(female ) / P( color blind )

= 0.0064*0.509 / 0.0425376

= 0.0766

Therefore 0.0766 is the required probability here