Educational attainment of couples. The table below shows the distribution of education level attained by US residents by gender based on data collected during the 2010 American Community Survey.60 Gender Male Female Less than 9th grade 0.07 0.13 9th to 12th grade, no diploma 0.10 0.09 Highest HS graduate (or equivalent) 0.30 0.20 education Some college, no degree 0.22 0.24 attained Associates degree 0.06 0.08 Bachelors degree 0.16 0.17 Graduate or professional degree 0.09 0.09 Total 1.00 1.00 (a) What is the probability that a randomly chosen man has at least a Bachelors degree? (b) What is the probability that a randomly chosen woman has at least a Bachelors degree? (c) What is the probability that a man and a woman getting married both have at least a Bachelors degree? Note any assumptions you must make to answer this question. (d) If you made an assumption in part (c), do you think it was reasonable? If you didnt make an assumption, double check your earlier answer and then return to this part.
Problem 2.11
Educational attainment of couples. The table below shows the distribution of education level attained by US residents by gender based on data collected during the 2010 American Community Survey.60 Gender Male Female Less than 9th grade 0.07 0.13 9th to 12th grade, no diploma 0.10 0.09 Highest HS graduate (or equivalent) 0.30 0.20 education Some college, no degree 0.22 0.24 attained Associates degree 0.06 0.08 Bachelors degree 0.16 0.17 Graduate or professional degree 0.09 0.09 Total 1.00 1.00
(a) What is the probability that a randomly chosen man has at least a Bachelor's degree?
(b) What is the probability that a randomly chosen woman has at least a Bachelor's degree?
(c) What is the probability that a man and a woman getting married both have at least a Bachelor's degree? Note any assumptions you must make to answer this question.
(d) If you made an assumption in part (c), do you think it was reasonable? If you didnt make an assumption, double check your earlier answer and then return to this part.
Step by Step Solution
Step 1 of 4
(a)
The table shows the distribution of education level attained by US residents by gender.The probability that a randomly chosen man has at least a Bachelor's degree can be written as, P(at least Bachelor’s Degree in men), ie;
P(at least Bachelor’s Degree in Men) = P(Bachelor’s Degree) + P(Graduate or professional degree)
P(at least Bachelor’s Degree in Men) = 0.16 + 0.09 = 0.25.
