Question

In Start City of all mens and วิ55 of all womens are color-blind. The 12 288 ratio of men and women is 1 : 1. Lets pick a random person. (a) A: Person is male, B: Person is color-blind. What are the probabilities of P(A), PA), P(BIA"), P(BIA) ? (b) Calculate P(B"A") and P(An B) (c) What is the total Probability, that a person is color blind (d) Let the selected person be color-blind. How big is the conditional probability, that the selected Person is male?

Answer 1

a)

no. of males = no. of females = X

Total = X + X = 2X

Probability(male) = P(A) = X / 2X = 0.5

P(A^c) = 1 - P(A)

= 0.5

Probability ( Blind and man ) = 0.5 * 1/12 = 1/24

Probability ( Blind and woman ) = 0.5 * 1/ 288

= 1/ 576

P ( B | A ) = P( B $\cap$ A ) / P(A)

= Probability ( Blind and man ) /  P(A)

= 0.5 * 1/12 / 0.5

= 1/12 = 0.0833

P ( B | A ^c) = P( B $\cap$ A^c ) / P(A^c)

= Probability ( Blind and woman ) / 0.5

=  0.5 * 1/ 288 / 0.5

= 1/288

=  0.0035

b)

P( A $\cap$ B ) = Probability ( Color blind male )

= 0.5 * 1/12 = 1/24

= 0.04167

c) P( colorblind) = 0.5 * 1/12 + 0.5*1/288

= 0.0434

d) P( Male | colorblind ) =  P( Male $\cap$ colorblind ) / P( colorblind)

= 1/24 /  0.0434

= 0.0018

Very small indeed.