Question

In 1970, 11% of americans completed four years of college; 43% of them were women. in 1990, 22% of americans completed four years of college; 53% of them were women (time, jan. 19, 1996). (a) given that a person completed four years 2 of college in 1970, what is the probability that the person was a woman? (b) what is the probability that a woman finished four years of college in 1990? (c) what is the probability that a man had not finished college in 1990?

Answer 1

a) 0.43

b) 0.1166

c) 0.8966

Explanation:

Percentage of people that completed 4 yrs college (1970) = 0.11

Women who passed 4 yrs college in 1970 = 43% of those (above)

Percentage of people that completed 4 yrs college (1990) = 0.22

Women who passed 4 yrs college in 1970 = 53% of those (above)

a)

It is already given in the question that of the people that passed college in 1970, 43% were women. This question already says that given that person completed 4 years college, how many are women??

That probability of that is 0.43

b)

Here, it is NOT given that who passed college. They want to know how many are women FROM THE PASSED ONES. So we need to multiply the percentages, 53% of 11%. That is:

0.53 * 0.22 = 0.1166

The probability is 0.1166

c)

We need to find the probability that MAN HAD FINISHED COLLEGE in 1990 and subtract that from 1 (as it is the complement).

Since 53% are women, that means 100% - 53% = 47% is man

Hence, MAN finishing college in 1990 = 0.47 * 0.22 = 0.1034

Subtract that from whole (1):

1 - 0.1034 = 0.8966

The probability is 0.8966