A random sample of 200 adults was selected from a large city

A random sample of 200 adults was selected from a large city. In this sample, 123 were men and 77 were women. Among the men, 83 were homeowners and 40 were renters. Among the women, 53 were homeowners. Suppose this sample is representative of the entire city. Find the probability that a randomly selected individual from this city is

A women and a renter.

A renter given the person is a man.

A renter given the person is a women.

Is gender independent of residence status? Why or why not?

Solution

a)A women and a renter. = 77-53=24

hence Proabability =24/200 =0.12

b) probabilityof A renter given the person is a man. = p(A renter + a man.)/p(man)

=40/123

c) probabilityof A renter given the person is a woman. = p(A renter + a woman.)/p(woman)

=24/77

d)P(man)Xp(renter) = p(man+renter)

=>123/200 X (40+24)/200 = 40/200

=>123X64 = 40X200

not equal...If the residence status and gender were independent then P(man)Xp(renter) = p(man+renter) should have been true....Hence they are not independent