Question

Suppose that 5% of all men and 0.25% of all women are color-blind. A person is chosen at random from a community having 55% women and 45% men. (a) What is the probability that the person is color-blind? (b) If the chosen person is color-blind, what is the probability that the person is male?

Answer 1

(a) Probability of male being color blind P(C|M)= 5% =0.05

Probability of female being color blind P(C|F) =0.25% =0.0025

Probability of male P(M) =45% =0.45

Probability of Female P(F) =55% =0.55

using the total theorem of Probability, we have,

Probability that person is Blind= P(C|M)* P(M)+ P(C|F) *P(F)  

=0.05*0.45+0.0025*0.55

=0.023875

(b) probability that the person is male can be obtained as follows:-

Given

P(C|M)=5%=0.05

P(C|F)=0.25%=0.0025

P(M)=45%=045

P(F)=55%=0.55

So Using the concept of Bayes theorem

probability that the person is male= P(C|M)*P(M) / [P(C|M)*P(M)+P(C|F)*P(F)]

=(0.45*0.05)/(0.45*0.05+0.55*0.0025)

=0.0225/0.023875

=0.94240838

# C- Color blind

#M=male

#F=female

#please feel free to ask any doubts. Thank You!!!