4. To gauge the relationship between education and unemployment, an economist turned to the US Census data to find the highest level of education attained by an individual respondent from which the following

(2 marks)

table of joint probabilities was

Highest level of Education Less than high school High school graduate Some college, no degree Associate's degree Bachelor's degree Advanced degree

produced:

Northeast Midwest 0.021 0.022 0.062 0.075 0.024 0.038 0.015 0.022 0.038 0.040 0.024 0.020

South 0.053 0.118 0.062 0.032 0.067 0.036

West 0.032 0.058 0.044 0.022 0.050 0.025

(a) Calculate the marginal probabilities for the given data

b) Find the probability that a person living in the West has a Bachelor's degree

(c) Find the probability that a high school graduate lives in the Northeast

(d) What is the probability that a person selected at random lives in the South?

(e) What is the probability that a person selected at random does not live in the South?

f) Given that someone lives in the South, what is the probability that they have a Bachelor's degree?

(g) Given that someone has a Bachelor's degree, what is the probability that they live in the South?