Question 874799: PROBEMS IN PROBABILITY
An experiment with three outcomes has been repeated 50 times, and E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use? Why?
A pharmaceutical company conducted a study to evaluate the effect of an allergy relief medicine;250 patients with symptoms that included itchy eyes and a skin rash received the new drug. The results of the study are as follows: 90 of the patients treated experienced eye relief, 135 had their skin rash clear up, and 45 experienced relief of both itchy eyes and the skin rash. What is the probability that a patient who takes the drug will experience relief of at least one of the two symptoms?
Suppose that a sample space has five equally likely experimental outcomes: E1 , E2, E3, E4, E5. Let
A ={E1, E2}, B = {E3, E4} , C = {E2, E3, E5}
a)Find P(A),P(B), and P(C)
b)Find P(AUB). Are A and B mutually exclusive?
c)Find Ac, Cc, P(Ac) and P(Cc)
d)Find AUBc and P(AUBc)
e)Find P(BUC)
4. A study of 100 students who had been awarded university scholarships showed that 40 had part-time jobs,25 had made the dean’s list the previous semester, and 15 had both a part-time job and made the dean’s list. What was the probability that a student had a part-time job or was on the dean’s list?
5. Let A be an event that a person’s primary method of transportation to and from work is an automobile and B be an event that a person’s primary method of transportation to and from work is a bus. Suppose that in a large city P(A) = 0.45 and P(B) = 0.35
a) Are events A and B mutually exclusive? What is the probability that a person uses an automobile or a bus in going to and from work?
b) Find the probability that a person’s primary method of transportation is some means other than bus.
6. A purchasing agent has placed a rush order for a particular raw material with two different suppliers, A and B. If neither order arrives in 4 days the production process must be shut down until at least one of the orders arrives. The probability that supplier A can deliver the material in 4 days is 0.55. The probability that supplier B can deliver the material in 4 days is 0.35.
a) What is the probability that both suppliers deliver the material in 4 days? Because two separate suppliers are involved, assume independence.
b) What is the probability that at least one supplier delivers the material in 4 days?
c)What is the probability the production process is shut down in 4 days because of a shortage
in raw material (i.e ,both orders are late)?
7. In the evaluation of sales training program, a firm discovered that of 50 salespeople receiving a bonus last year, 20 had attended a special sales training program. The firm has 200 salespeople. Let B = the event that a salesperson makes a bonus and S = the event that a salesperson attends the sales training program.
a) Find P(B), P(S/B) and P(S∩B)
b) Assume that 40 % of the salespeople have attended the training program. What is the probability that a salesperson makes a bonus given that the salesperson attended the sales training program, P(B/S)?
c) If the firm evaluates the training program in terms of its effect on the probability of a salesperson’s receiving a bonus, what is your evaluation of the training program? Comment on whether B and S are dependent or independent events
8. A consulting firm has submitted a bid for a large research project. The firm’s management initially felt there was a 50-50 chance of getting the bid. However, the agency to which the bid was submitted has subsequently requested additional information on the bid. Experience indicates that on 75 % of the successful bids and 40 % of the unsuccessful bids the agency requested additional information.
a) What is the prior probability the bid will be successful (i.e. prior to receiving the request for additional information)?
b) What is the conditional probability of a request for additional information given that the bid will ultimately be successful?
c) compute a posterior probability that the bid will be successful given that a request for additional information has been received.
9. The Wayne manufacturing company purchases a certain part from suppliers A, B and C. Supplier A supplies 60 % of the parts, B 30 % and c 10%. The quality of parts varies among the suppliers, with A, B and C parts having 0.25%, 1% and 2% defective rates, respectively. The parts are used in one of the company’s major products.
a)What is the probability that the company’s major product is assembled with a defective part? Use the tabular approach to Bayes theorem to solve.
b)When a defective part is found, which supplier is the likely source?
10. In a survey of MBA students , the following data were obtained on “students” first reason for application to the school in which they matriculated.
Reason for Application
School School cost
Quality or Convenience other Totals
Enrollment Full time 421 393 76 890
Status Part time 400 593 46 1039
Totals 821 986 122 1929
a)Develop a joint probability table using these data.
b) Use a marginal probabilities of school quality , school cost or convenience and other to comment on the most important reason for choosing a school
c)If a student goes full time, What is the probability that school quality will be the first reason for choosing a school?
d) If a student goes part time,. What is the probability that school quality will be the first reason for choosing a school?
e) Let A be the event that a student is full time and let B be the event that the student lists school quality as the first reason for applying. Are events A and B independent? Justify your answer.
Answer by ewatrrr(24785)   (Show Source):
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