91Ó°ÊÓ

In \(1970,11 \%\) of Americans completed four years of college; \(43 \%\) of them were woman. 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 of college in 1970 , what is the probability that the person was a women? (b) What is the probability that a woman would finish four years of college in \(1990 ?\) (c) What is the probability that in 1990 a man would not finish college?

A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If \(40 \%\) of these homes are usually left unlocked. what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office"

Before the distribution of certain statistical software every fourth compact disk (CD) is tested for accuracy. The testing process consists of running four independent programs and checking the results. The failure rate for the 4 testing programs are. respectively, \(0.01,0.03,0.02,\) and 0.01 (a) What is the probability that a CD was tested and failed any test? (b) Given that a CD was tested, what is the probability that it failed program 2 or \(3 ?\) (c) In a sample of 100 , how many CDs would you expect to bo rejected? (d) Given a CD was defective, what is the probability that it, was tested?

A town has 2 fire engines operating independently. The probability that a specific engine is available when needed is 0.96 . (a) What is the probability that neither is available when needed? (b) What is the probability that a fire: engine is available when needed?

The probability that Tom will be alive in 20 years is \(0.7,\) and the probability that Nancy will be alive in 20 years is 0.9 . If we assume independence for both. what is the probability that neither will be alive in 20 years?

One overnight case contains 2 bottles of aspirin and 3 bottles of thyroid tablets. A second tote bag contains 3 bottles of aspirin, 2 bottles of thyroid tablets, and I bottle of laxative tablets. If 1 bottle of tablets is taken at random from each piece of luggage, find the probability that (a) both bottles contain thyroid tablets: (b) neither bottle contains thyroid tablets; (c) the 2 bottles contain different tablets.

The probability that a person visiting his dentist will have an X-ray is \(0.6 ;\) the probability that a person who has an X-ray will also have a cavity filled is \(0.3 ;\) and the probability that a person who has had an X-ray and a cavity filled will also have a tooth extracted is 0.1 . What is the probability that a person visiting his dentist will have an X-ray, a cavity filled, and a tooth extracted?

In a certain region of the country it is known from past experience that the: probability of selecting an adult over 40 years of age: with cancer is \(0.05,\) If the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the: probability of incorrectly diagnosing a person without cancer as having the disease is \(0.06,\) what is the probability that, a person is diagnosed as having cancer?

Police plan to enforce speed limits by using radar traps at 4 different locations within the city limits. The radar traps at each of the locations \(L L L_{2}\). \(L_{3},\) and \(L_{4}\) are operated \(40 \%, 30 \%, 20 \%,\) and \(30 \%\) of the time, and if a person who is speeding on his way to work has probabilities of \(0.2,0.1,0.5,\) and \(0.2,\) respectively, of passing through these locations, what is the probability that he will receive a speeding ticket?

Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps \(20 \%\) of the packages, fails to stamp the expiration date once in every 200 packages; Tom, who stamps \(60 \%\) of the packages, fails to stamp the expiration date once in every 100 packages; Jeff, who stamps \(15 \%\) of the packages, fails to stamp the expiration date once in every 90 packages; and Pat, who stamps \(5 \%\) of the packages, fails to stamp the expiration date once in every 200 packages. If a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John?