Exam 4: Introduction to Probability

The Board of Directors of Bidwell Valve Company has made the following estimates for the upcoming year's annual earnings: P(earnings lower than this year) = .30 P(earnings about the same as this year) = .50 P(earnings higher than this year) = .20 After talking with union leaders, the human resource department has drawn the following conclusions: P(Union will request wage increase | lower earnings next year) = .25 P(Union will request wage increase | same earnings next year) = .40 P(Union will request wage increase | higher earnings next year) = .90 a. Calculate the probability that the company earns the same as this year and the union requests a wage increase. b. Calculate the probability that the company has higher earnings next year and the union does not request a wage increase. c. Calculate the probability that the union requests a wage increase.

A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

A(n) __________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles.

Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3. a.What is the probability that you will receive a Merit scholarship? b.Are events A and M mutually exclusive? Why or why not? Explain. c.Are the two events, A and M, independent? Explain, using probabilities. d.What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? e.What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?

Tammy is a general contractor and has submitted two bids for two projects (A and B). The probability of getting project A is 0.65. The probability of getting project B is 0.77. The probability of getting at least one of the projects is 0.90. a.What is the probability that she will get both projects? b.Are the events of getting the two projects mutually exclusive? Explain, using probabilities. c.Are the two events independent? Explain, using probabilities.

Given that event E has a probability of 0.25, the probability of the complement of event E

Through a telephone survey, a low-interest bank credit card is offered to 400 households. The responses are as follows. a. Develop a joint probability table and show the marginal probabilities.. b. What is the probability of a household whose income exceeds $50,000 and who rejects the offer? c. If income is < $50,000, what is the probability the offer will be accepted? d. If the offer is accepted, what is the probability that income exceeds $50,000?

Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are independent of each other. a.What is the probability that you will be accepted in both universities? b.What is the probability that you will be accepted to at least one graduate program? c.What is the probability that one and only one of the universities will accept you? d.What is the probability that neither university will accept you?

Sixty percent of the student body at UTC is from the state of Tennessee (T), 30% percent are from other states (O), and the remainder is international students (I). Twenty percent of students from Tennessee live in the dormitories, whereas 50% of students from other states live in the dormitories. Finally, 80% of the international students live in the dormitories. a.What percentage of UTC students lives in the dormitories? b.Given that a student lives in the dormitory, what is the probability that she/he is an international student? c.Given that a student does not live in the dormitory, what is the probability that she/he is an international student?

The Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is

An applicant has applied for positions at Company A and Company B. The probability of getting an offer from Company A is 0.4, and the probability of getting an offer from Company B is 0.3. Assuming that the two job offers are independent of each other, what is the probability that a.the applicant gets an offer from both companies? b.the applicant will get at least one offer? c.the applicant will not be given an offer from either company? d.Company A does not offer the applicant a job, but Company B does?

Any process that generates well-defined outcomes is

The multiplication law is potentially helpful when we are interested in computing the probability of

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is

An investment advisor recommends the purchase of shares in Infogenics, Inc. He has made the following predictions: P(Stock goes up 20% | Rise in GDP) = .6 P(Stock goes up 20% | Level GDP) = .5 P(Stock goes up 20% | Fall in GDP) = .4 An economist has predicted that the probability of a rise in the GDP is 30%, whereas the probability of a fall in the GDP is 40%. a. Draw a tree diagram to represent this multiple-step experiment. b. What is the probability that the stock will go up 20%? c. We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP?

Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on business while on ordinary jets 30% of the passengers are on business. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. (Hint: you have been given two conditional probabilities.) a. What is the probability a randomly chosen business customer flying with Global is on a jumbo jet? b. What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?

If a coin is tossed three times, the likelihood of obtaining three heads in a row is

Two events are mutually exclusive if

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is