Exam 3: Probability

Are the sales price and time on market statistically independent? Explain.

If events A and B are mutually exclusive,then events and must be mutually exclusive.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: You stop in at a local Internet café.The manager tells you that there are four computers in the cafe,and that the probability for one of them being available at any one time is 0.4.Assume that this probability is the same for each computer and the probability of one computer being occupied is statistically independent of any of the other computers. -What is the probability that at least one computer is available?

In a recent article it was reported that 35.4% of all high school students smoke cigarettes.65% of these students plan on going to college.What is the probability that a randomly selected student smokes cigarettes and plans on going to college?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: James' Surfboard Shop makes surfboards by hand.The number of surfboards that James makes during a week depends on the wave conditions.James has estimated the following probabilities for surfboard production for the next week. Let A be the event that James produces more than seven surfboards.Let B be the event that James produces exactly six surfboards. -What is the probability of event A?

Suppose A and B are two events where P(A)= 0.3,P(B)= 0.4,and P(A ∩B)= 0.15.Then,P(A |B)= 0.3.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A company wishes to evaluate the effectiveness of a marketing campaign.Seventy five percent of all potential professors were reached in a focused advertising program.Twenty eight percent of those contacted adopted the book while 8% of the adoptions came from professors who did not receive the promotional material.Define the following events of interest: A₁ = Professor received advertising material A₂ = Professor did not receive advertising material B₁ = Professor adopts the book B₂ = Professor does not adopt the book -What is the probability that a professor adopts the book?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A recent survey showed that 15% of computer programmers have experienced some form of wrist pain from typing,and that 25% are taking aspirin daily.Six percent of all programmers have both experienced some form of wrist pain from typing and taken aspirin on a daily basis. -What is the probability that a programmer has wrist pain or takes aspirin on a daily basis?

Permutations are employed in cases where the order of objects is not important.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A stock analyst has provided estimates of a corporation's expected return over the next year.This return is likely to depend on the interest rate,so the analyst has developed the following two-way table. -What is the probability that either the corporation's return is less than 12% or the interest rate is at least 3% or both?

A research project on retention at a large university indicated that 20% of the students had a problem with stress while 25% reported problems with financial resources and 15% had a problem with both.What is the probability that a particular student has a problem with either stress or financial resources?

A sales representative calls on five hospitals in Utah County.It is immaterial in what order he calls on them.How many ways can he organize his calls?

If two events are collectively exhaustive,they must also be mutually exclusive.

What is P(B |A)?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A recent survey examined the working arrangements of married households.It was found that 88% of the households had at least one working member.In 20% of the households with the woman not working,the man also does not work.In 40% of households in which the man doesn't work,the woman also does not work. -What is the probability that the man doesn't work and the woman works?

How would you explain to your boyfriend or girlfriend (I know they are intelligent people!)who have not studied probability at all the difference between mutually exclusive events and independent events? Illustrate your answer with easy to understand examples.

The probability of the intersection of two events cannot be greater than either of their individual probabilities.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A recent survey examined the working arrangements of married households.It was found that 88% of the households had at least one working member.In 20% of the households with the woman not working,the man also does not work.In 40% of households in which the man doesn't work,the woman also does not work. -What is the probability that both man and woman are working?

The relative frequency probability is the limit of the proportion of times that an event occurs in a large number of trials.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A personnel officer for a firm that employs many part time salespeople tries out a sales aptitude test on several hundred applicants.Because the test is unproven,results are not used in hiring.Forty percent of applicants show high aptitude on the test and 12% of those hired both show high and achieve good sales records.The firm's experience shows that 30% of all salespeople achieve good sales.Let A be the event "shows high aptitude" and let B be the event "achieves good sales". -What is P(A)?