Exam 3: Probability

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The joint probabilities shown in a table with two rows,A₁ and A₂,and two columns,B₁ and B₂ are as follows: P(A₁ ∩ B₁)= 0.10,P(A₁ ∩ B₂)= 0.30,P(A₂ ∩ B₁)= 0.05,P(A₂ ∩ B₂)= 0.55 -What is P(A₂ |B₁),rounded to two decimals?

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 who received advertising material does not adopt the book?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features. -The probability that a person wants a vehicle navigation system given that he wants a better fuel efficiency is approximately:

Which of the following applications would an auditor apply to determine the probability of a corporation's account balance being in error?

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. -Are eating lunch at the company cafeteria and gender of a randomly chosen employee mutually exclusive events?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose you roll a pair of dice.Let A be the event that you observe an even number.Let B be the event that you observe a number greater than seven. -What is A ∪ ?

The sum of the probabilities of collectively exhaustive events must equal 1.

The probability of the union of two events cannot be more than the sum of their individual probabilities.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a recent survey about capital punishment,64% of the respondents said that they support capital punishment.Females comprised 48% of the sample,and of the females,46% supported capital punishment. -What is the probability that a randomly selected person is a male and does not support capital punishment?

Are the events A and B independent? Explain.

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 who does not receive advertising material has not adopted the book?

When events have no common basic outcomes,they are said to be:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A table of joint probabilities is shown below,regarding the instructors at the University of Michigan,where the events A_i(i = 1,2,3)and B_j (j = 1,2)are defined as follows: A₁ = Full professor,A₂ = Associate professor,A₃ = Assistant professor,B₁ = Male instructor,and B₂ = Female instructor. -Calculate P(B₂ ∣ A₁).

A gumball machine has five different colored gumballs: red,blue,white,green,and yellow.If you buy three gumballs,how many different combinations of colors could you buy?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The production manager at a local manufacturing plant is concerned about work stoppages in the four production lines.In particular,the manager is evaluating the likelihood of the next stoppage occurring on production line 1. -Based on his knowledge of the causes of stoppages,the manager states that the probability that production line 1 is stopped next is 25%.This is an example of:

What is the probability of the intersection of events A and B?

If a plane has just left on time,what is the probability that it was airline B?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A table of joint probabilities is shown below,regarding the instructors at the University of Michigan,where the events A_i(i = 1,2,3)and B_j (j = 1,2)are defined as follows: A₁ = Full professor,A₂ = Associate professor,A₃ = Assistant professor,B₁ = Male instructor,and B₂ = Female instructor. -Calculate P(A₂ ∣ B₁).

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features. -The probability that a person wants either better fuel efficiency or a vehicle navigation system is:

Two events A and B defined on a sample space S are said to be collectively exhaustive if: