Question

In the 1996 General Social Survey, for males age 30 and over, the following was true about respondents: • 11% of those in the lowest income quantile were college graduates. • 19% of those in the second income quantile were college graduates. • 31% of those in the third income quantile were college graduates. • 53% of those in the highest income quantile were college graduates. Find P(Q1|G), the probability that a randomly selected college graduate falls in the lowest income quartile. Also find P(Q2|G), P(Q3|G), and P(Q4|G). Discuss how this distribution compares to the unconditional distribution P(Q1), P(Q2), P(Q3), P(Q4)

Answer 1

Let

Q1 = male those in lowest income quantile

Q2 = male those in second income quantile

Q3 = male those in third income quantile

Q4 = male those in highest income quantile

G = male those are college graduate

Unconditional probability doesn't depend on other events but in conditional probability depend on the other event P(Q1) means the probability of males to be in lowest income quantiles these may include college graduate and also nongraduates .The same happens to Q2 , Q3 and Q4 their probabilities now include both graduates and nongraduates and that is unconditional and given as P(Q2) , P(Q3) , P(Q4) .