Assume that for two events A and B, P(A) = 0.80, P(A|B) = P(A), and P(C|A) = 0.85. Is this a consistent assignment of probabilities?
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At a soup kitchen, a social worker gathers the following data. Of those visiting the kitchen, 59 percent are men, 32 percent are alcoholics, and 21 percent are male alcoholics. What is the probability that a random male visitor to the kitchen is an alcoholic?
During a study of auto accidents, the Highway Safety Council found that 60 percent of all accidents occur at night, 52 percent are alcohol-related, and 37 percent occur at night and are alcohol-related.
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If a hurricane forms in the eastern half of the Gulf of Mexico, there is a 76 percent chance that it will strike the western coast of Florida. From data gathered over the past 50 years, it has been determined that the probability of a hurricane's occurring in this area in any given year is 0.85.
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Al Cascade, president of the Litre Corporation, is studying his company's chances of being awarded an impotent water purification system contract for the Tennessee Valley Authority. Accordingly, two events are of interest to him. First, Litre's major competitor, WTR, is conducting purification research, which it hopes to complete before the contract award deadline.
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A company is considering upgrading its computer system and a major portion of the upgrade is new operating system. The company has asked an engineer for an evaluation of the operating system. Suppose the probability of a favorable evaluation is 0.65. If the probability the company will up-grade its system given a favorable evaluation is 0.85, what is the probability that the company will upgrade and receive a favorable evaluation?
The university's library has been randomly surveying patrons over the last month to see who is using the library and what services they have been using. Patrons are classified as undergraduate, graduate, or faculty. Services are classified as reference, periodicals, or books. The data for 350 people are given below Assume a patron uses only service per visit.
Find the probability that a randomly chosen patron
- Is a graduate student?
- Visited the periodicals section, given the patron is a graduate student?
- Is a faculty member, given a reference section visit?
- Is an undergraduate who visited the book section
The southeast regional manager of General Express, a parcel-delivery firm, is worried about the likelihood of strikes by his pilots is 0.75 and the probability of a strike by his drivers is 0.65. Further, he knows that if the drivers strike, there is a 90 percent chance that the pilots will strike in sympathy.
- What is the probability of both groups’ striking?
- If the pilots strike, what is the probability that the drivers will strike in sympathy?
Given: The probabilities of three events, A, B, and C, occurring are P(A)= 0.35, P(B)= 0.45, and P(C)=0.2. Assuming that A,B,or C has occurred, the probabilities of another event, X, occurring are P(X|A) = 0.8, P(X|B) = 0.65, and P(X|C) = 0.3. Find P(A|X), P(B|X), and P(C|X).
A doctor has decided to prescribe two new drugs to 200 heart patients as follows: 50 get drug B, and 100 get both. The 200 patients were chosen so that each had an 80 percent chance of having a heart attack if given neither drug. Drug A reduces the probability of a heart attack by 35 percent drug B reduces the probability by 20 percent, and the two drugs when taken together, work independently. If a randomly selected patient in the program has a heart attack, what is the probability that the patient was both drugs?