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)
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 )]