In: Statistics and Probability
The following data are from the Bureau of Labor Statistics and shows the outcome of women at age 46:
Less than High school
High school grad
Some college
Bachelor’s degree +
Ever Married
0.09
0.30
0.23
0.24
Ever Divorced
0.05
0.15
0.11
0.07
Never Married
0.02
0.05
0.03
0.04
Note that ever married and ever divorced are not mutually exclusive—the ”ever divorced” category is a subset
of the ”ever married” category.
(a) What percent of women were ever married?
(b) What percent of women have a bachelor’s degree or higher?
(c) If a woman has been divorced, what’s the probability that she has less than a high school diploma or is a
high school graduate with no college?
(d) My sister is getting married this summer. According to this data, what’s the unconditional probability she
gets divorced? (i.e. what’s the probability she gets divorced if we don’t factor in her education level?)
(e) What’s the probability my sister gets divorced given she has a Bachelor’s degree?
(f) Is divorce rate independent of education level?
Ever Married | Ever Divorced | Never Married | |
Less than High School | 0.09 | 0.05 | 0.02 |
High School Grad | 0.30 | 0.15 | 0.05 |
Some College | 0.23 | 0.11 | 0.03 |
Bachelor's degree + | 0.24 | 0.07 | 0.04 |
Question (a)
% of Women that are ever married = 0.09+0.30+0.23+0.24
= 0.86
= 86%
Question (b)
% of women that have bachelor's degree or higher = 0.24 (ever married) + 0.04(Never married) = 0.28 = 28%
ever divorced is not considered since it is a subset of ever married
Question (c)
If a women has been divorced, probability that she has less than a high school diploma or is a high school graduate with no college?
probability that she has less than a high school diploma = 0.05
probability that she s a high school graduate with no college = 0.15
probability that she has less than a high school diploma or is a high school graduate with no college = 0.05 + 0.15 = 0.2
Question (d)
The unconditional probability she gets divorced = 0.05 + 0.15 + 0.11 +0.07 = 0.38
Question (e)
Here we should use conditional probability
Probability (She gets divorced given she has a bachelor's degree)
= Probability (she is divorced and has a bachelor's degree) / Probability (she has a bachelors degree)
= 0.07/ 0.28
= 0.25
Question (f)
divorce rate is not independent of education level since the probabilities of divorce are different for different educational degrees or levels