Question

A crowd of people is in a room. One person from the room is selected randomly. Suppose that we know that 1/5 of the people are over six feet tall. 1/8 of the people have green eyes. The probability that we select someone with either green eyes or who is over six feet tall is given by P(T union G) = 0.25

a. Find the probability that the person selected has green eyes and is taller than six feet.

b. Find the probability that the person selected has green eyes and is shorter than six feet.

c. Find the probability that the person selected has green eyes given that the person is over six feet tall.

Answer 1

here probability of people over 6 feet tall =P(T) =1/5

probability of people with green eyes =P(G) =1/8

P(TUG) =0.25

hence

a) probability that the person selected has green eyes and is taller than six feet

=P(TnG) =P(T)+P(G)-P(TUG) =(1/5)+(1/8)-0.25=0.075

b) probability that the person selected has green eyes and is shorter than six feet

=P(G)-P(TnG) =(1/8)-0.075=0.05

c)  probability that the person selected has green eyes given that the person is over six feet tall

=P(G|T) =P(TnG)/P(T)=0.075/(1/5)= 0.375