33 let event a be that there are more than three

33. Let event A be that there are more than three defects and let event B be that there are four
or fewer defects. Which of the following statements is true?
A) P (
A B 
) = 0.18
B) P (
A B 
) = 0.07
C) events A and B are collectively exhaustive
D) events A and B are mutually exclusive
ANSWER: C
34. Let event A be that there are more than two defects and let event B be that there are four
or fewer defects. Which of the following statements is true?
7

35. Let A be the event that there is at least one defect and let event B be that there is at most
three defects. Which of the following statements is true?
36. A gumball machine has five different colored gumballs: red, blue, white, green, and
yellow. If you buy 3 gumballs, how many different combinations of colors could you
buy?
THE NEXT FOUR 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.
37. What is the probability that the class was taught by a professor with poor evaluations and
that the student enjoyed the class?
38. What is the probability that the class was taught by a professor with good evaluations and
that the student enjoyed the class?
B ) =
39. What is the probability that the student enjoyed the class given that it was taught by a
professor with good evaluations?
8

Event A : Student enjoyed class
Event B : Class taught by professors with good evaluations
P ( B ) = 0.84
P ( A | B ) = P( A

B ) / P ( B ) = 0.609/0.84 = 0.725
40. Suppose a student signed up for three courses next semester, all of which are taught by
professors with good evaluations. What is the probability he enjoys all three?
THE NEXT NINE 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.
41. What is the probability that the person we select is female and supports U.S. policy in Iraq?