Exam 3: Probability

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A student has access to professor evaluations.Overall,he has enjoyed 70% of all classes he has taken.He finds that of the courses he has enjoyed,13% were taught by professors with poor evaluations.84% of the courses he has taken were taught by professors with good evaluations. -What is the probability that the student enjoyed the class given that it was taught by a professor with good evaluations?

An event and its complement are mutually exclusive.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The probability that an employee at a company eats lunch at the company cafeteria is 0.23,and the probability that employee is female is 0.52.Assume the probability that an employee eats lunch at the company cafeteria and is female is 0.11. -The probability that a new small business closes before the end of its first year is 42%.In addition,37% of all new businesses are started by women.The probability that a new business is either owned by a woman or goes out of business is 62%.Your sister starts a new business.What is the probability her business will still open at the end of the first year?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a survey of top executives,it was found that 46% had either traveled internationally on business or could fluently speak a foreign language.The probability that an executive who had not traveled internationally could speak a foreign language was 10%.It was found that only 4% of the executives had traveled internationally and could speak a foreign language. -What is the probability that an executive has not traveled internationally and could speak a foreign language fluently?

If P(A ∩B)= P(A)P(B),then A and B must be statistically independent.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The probability that interest rates on housing loans will go up in the next 6 months is estimated to be 0.20.The probability that house sales will decrease is estimated to be 0.6.The probability that interest rates will go up and house sales will decrease is estimated to be 0.15. -The probability that interest rates increase and house sales decrease is:

Which of the following statements is not true?

To determine the effectiveness of a new advertisement which is shown to one customer group and not another,followed by observation of the purchase behavior of both groups is determined by the use of:

The conditional probabilities P(A |A)are always equal.B)and P(B |

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A review of the personnel records of a small corporation has revealed the following information about the number of sick days taken per year and the corresponding probabilities. Let A be the event that an employee takes more than 2 sick days.Let B be the event that an employee takes less than five sick days. -What is the probability of event A?

Events A and B are said to be statistically independent if their intersection is the empty set.

The probability of the intersection of events A and B is denoted by:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A general contractor has submitted two bids for two projects;A and B.The probability of getting project A is 0.60.The probability of getting project B is 0.75.The probability of getting at least one of the projects is 0.85. -What is the probability that the contractor will get both projects?

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?

A subset of outcomes is defined as a(n):

When a problem arises in counting the numbers of basic outcomes in the sample space and the event of interest to compute the probability of an event,it is helpful to use:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Given A= {E₃,E₄,E₈,E₁₀} and B = {E₃,E₄,E₆,E₉} -What is the union of A and B?

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". -Are A and B independent?

If E₁,E₂,….. ,E_k are collectively exhaustive events,then the probability of their union is always smaller than 1.

A Tree-branch model is particularly useful when there's only one event of interest.