The table below shows the distribution of education level at

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: What is the probability that a randomly chosen man has at least a Bachelor\'s degree? What is the probability that a randomly chosen woman has at least a Bachelor\'s degree 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. If you made an assumption in part (c), do you think it was reasonable? If you didn\'t make an assumption, double check your earlier answer and then return to this part.

Solution

a) P[ a randomly chosen man has atleast a Bachelor\'s degree]

0.16 + 0.09 = 0.25

b)  P[ a randomly chosen woman has atleast a Bachelor\'s degree]

0.17+0.09= 0.26

c)  When two events are said to be independent of each other, what this means is that theprobability that one event occurs in no way affects the probability of the other eventoccurring.

Assuming that the education level of the husband and wife are independent:

0.25*0.26 = 0.065

We might also notice that we actually made a second assumptions:

that the decision to get married is unrelated to education level.

d) The husband and wife independence assumption is probably not reasonable, because people often marry another person with a comparable level of education.

We will leave it on own decision to think about whether the second assumption noted in part c) is reasonable.