91Ó°ÊÓ

Twelve people: are given two identical speakers to listen to for differences, if any. Suppose that these people answered by guessing only. Find the probability that three people claim to have heard a difference between the two speakers.

In a certain city district the need for money to buy drugs is stated as the reason for \(75 \%\) of all thefts. Find the probability that among the next 5 theft cases reported in this district, (a) exactly 2 resulted from the need for money to buy drugs; (b) at most 3 resulted from the need for money to buy drugs.

According to Chemical Engineering Progress (Nov. 1990), approximately \(30 \%\) of all pipework failures in chemical plants are caused by operator error. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? (c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 5 are operational errors. Do you feel that the \(30 \%\) figure stated above applies to this plant? Comment.

One prominent physician claims that \(70 \%\) of those with lung cancer are chain smokers. If his assertion is correct, (a) find the: probability that of 10 such patients recently admitted to a hospital, fewer than half are chain smokers: (b) find the probability that of 20 such patients recently admitted to a hospital, fewer than half are chain smokers.

According to a study published by a group of University of Massachusetts sociologists, approximately \(60 \%\) of the Valium users in the state of Massachusetts first took Valium for psychological problems. Find the probability that among the next 8 users interviewed from this state, (a) exactly 3 began taking Valium for psychological problems; (b) at least 5 began taking Valium for problems that were not psychological.

A nationwide survey of seniors by the University of Michigan reveals that almost \(70 \%\) disapprove of daily pot smoking, according to a report in Parade. If 12 seniors are selected at random and asked their opinion, find the probability that the number who disapprove of smoking pot daily is (a) anywhere from 7 to 9 : (b) at most 5 ; (c) not less than 8 .

The probability that a patient recovers from a delicate heart operation is 0.9 . What is the probability that exactly 5 of the next 7 patients having this operation survive?

A traffic control engineer reports that. \(75 \%\) of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles arc from out of state?

It is known that \(60 \%\) of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that (a) none contracts the discase: (b) fewer than 2 contract the disease; (c) more than 3 contract the disease.

Suppose that airplane engines operate independently and fail with probability equal to 0.4. Assuming that a plane makes a safe flight if at least one-half of its engines run, determine whether a 4 -engine plane or a 2 engine plane has the higher probability for a successful flight.