To gauge the relationship between education and unemployment an economist turned to the US Census, from which the following table was produced:

(First number represents employed, second number represents unemployed)

Not a high school graduate 0.0975 , 0.0080

High school graduate 0.3108 , 0.0128

Some college, no degree 0.1785 , 0.0062

Associate’s degree 0.0849 , 0.0023

Bachelor’s degree 0.1959 , 0.0041

Advanced degree 0.0975 , 0.0015

a. What is the probability that a high school graduate is unemployed?

b. Determine the probability that a randomly selected individual is employed.

c. Find the probability that an unemployed person possesses an advanced degree.

d. What is the probability that a randomly selected person did not finish high school?

Data from the Office on Smoking and Health, Centers for Disease Control and Prevention, indicate that 40% of adults who did not finish high school, 34% of high school graduates, 24% of adults who completed some college (no degree), and 14% of graduates (Degree holders) smoke.

e. Suppose that one individual is selected at random and it is discovered that the individual smokes. What is the probability that the individual is a graduate? (Use the probabilities from the table above to solve this question)

HINT:

Conditional probability: P(A|B) = P(A and B)/P(B)

Bayes’ Law Formula:

P(Ai |B)= ]P(Ai)P(B|Ai)] / [P(A1 )P(B | A1 ) + P(A 2 )P(B | A 2 ) + . . . + P(A k )P( B | A k )]