Question

A US Census American Housing Survey studies how US homeowners get to work, the survey consists of 1,000 homeowners and 1,000 renters. The result is:
Drivers to work Home Owners Renters Totals
Yes 824 681 1505
No 176 319 495
Total 1000 1000 2000
a) Given that the respondent drives to work, what is the probability that he or she is a home owners?
b) Given that the respondent is a homeowner, what is the probability that he or she drives to work?

Answer 1

Condition

A US Census American Housing Survey studies how US homeowners get to work, the survey consists of 1,000 homeowners and 1,000 renters. The result is: Drivers to work Home Owners Renters Totals Yes 824 681 1505No 176 319 495Total 1000 1000 2000a) Given that the respondent drives to work, what is the probability that he or she is a home owners? b) Given that the respondent is a homeowner, what is the probability that he or she drives to work?

Solution

a) Given that the respondent drives to work, what is the probability that he or she is a home owners?

$$P = \frac{824}{824 + 681} = 0.54750830564784053156146179401993$$

b) Given that the respondent is a homeowner, what is the probability that he or she drives to work?

$$P = \frac{824}{824 + 176} = 0.824$$