1. The following table, based on the data from the Centers for Disease Control, gives the number of new cases of the AIDS virus for men and women in the United States in 1998 by method of transmission.
Method of Transmission Male Female Total
Homosexual contact 8388 0 8388
Heterosexual contact 1146 1806 2952
Intravenous drug use 3652 1541 5193
Other 5237 2054 7291
Total 18423 5401 23824
a. Find the probability that a male resident who was newly diagnosed with AIDS in 1998 contracted it via homosexual contact.
b. Find the probability that a female resident who was newly diagnosed with AIDS in 1998 contracted it via intravenous drug use.
2. A company sells printers and copiers. Let E be the event "a customer buys a printer," and let F be the event "a customer buys a copier." Write the following use Intersection (upsidedown U), Union(U), or ' as necessary.
a. A customer buys neither machine.
b. A customer buys at least one of the machines.
3. The probability that a certain machine turns out a defective item is .05. Find the probabilities that in a run of 75 items, the following results are obtained.
a. Exactly 5 defective items
b. No defective items
c. At least 1 defective item
4. In a club with 20 senior and 10 junior members, what is the expected number of junior members on a 3-member committee?
Probability and events are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.