Exam 3: Probability

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 traveled internationally and could not speak a foreign language fluently?

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(B₂)?

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

A tree diagram is very useful for portraying prior,conditional,and joint probabilities.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a recent survey about US policy in Iraq,62 % of the respondents said that they support US policy in Iraq.Females comprised 53% of the sample,and of the females,46% supported US policy in Iraq.A person is selected at random. -What is the probability that the person we select is female and does not support US policy in Iraq?

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

A random experiment is a process leading to two or more possible outcomes.

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(A₁ ∣ B₁).

A junior executive looking at his business attire in his closet notes that he has five suits,six shirts,and three pairs of shoes.He is going on a business trip and needs to take two of each.How many different combinations of outfits could he take?

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 woman doesn't work?

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 who has traveled internationally speaks a foreign language fluently?

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(A₁ ∣ A₂).

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Three airlines serve a small town in Indiana.Airline A has 60% of all the scheduled flights,airline B has 30%,and airline C has the remaining 10%.Their on-time rates are 80%,60%,and 49% respectively.Define event D as an airline arrives on time. -Calculate P(A andD).

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A multiple choice quiz has five questions,each with five answers,A through E.Assume you just guess on all of the questions. -What is the probability that you get exactly three questions right?

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 does not speak a foreign language fluently?

What is P(A ∩ )?

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 ∩ ?

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 does not adopt the book?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a sample space defined by events A₁,A₂,B₁,B₂.Let P(A₁)= 0.40 ,P(B₁ ∣ A₁)= 0.60 and P(B₁ ∣ A₂)= 0.70 -What is P(A₂ ∩ B₁)?

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(A₁|B₂),rounded to two decimals?