HW1-1

Stat 200 HW1 Fall 2022 Section #: Name: 1. Mix and Match the item from the first column to the best item from the second.

Stat 200 HW1 Fall 2022 2. Mark each statement True or False. If you believe that a statement is false, briefly say why you think it is false. Exercises 11-16. A market research assistant watches the next five customers as they leave the store. He records whether the customer is carrying a store bag that indicates the customer made a purchase. He writes down a yes or a no for each. Define the events. A = { first two shoppers have a bag } B = { last two shoppers have a bag } C = { last three shoppers have a bag } • 13. P ( A ) + P ( B ) = P ( A ∪ B ) . • 14. The probability that both events B and C occur is equal to P(B). • 15. The probability that a randomly chosen customer purchases with a credit card or spends more than $50 is the same as or larger than the probability that the customer purchases with a credit card and spends more than $50. Exercises 17-22. The Human Resources (HR) group at a large accounting firm in- terviews prospective candidates for new hires. After each interview, the firm rates the candidate on a 10-point scale, with the rating 10 denoting exceptionally good candidates and 1 denoting those that the firm rates poor. The HR group rated 6 can- didates on Monday and 6 candidates on Tuesday. The outcomes of these 12 ratings form the sample space. • 18. If 8 of the 12 candidates on Monday and Tuesday rate above 6, then the probability of a candidate rating above 6 on Wednesday is 8/12. • 20. The probability that the ratings of the six candidates on Monday are { 6, 4, 3, 8, 11, 8 } is zero. • 21. Define the events A = { 6 out of the 12 candidates rate 8 or better } , B = { 3 out of the 6 candidates on Monday rate 8 or better } , and C = { 3 out of the 6 candidates on Tuesday rate 8 or better } The independence between B and C implies that P(A)=P(B)*P(C)

Stat 200 HW1 Fall 2022 3. A credit-rating agency assigns ratings to corporate bonds. The agency rates bonds offered to companies that are most likely to honor their liabilities AAA. The ratings fall as the company becomes more likely to default, dropping from AAA to AA, A, down to BBB,BB, B, CCC, CC, R, and then D (for in default). Let the event W = { AAA, AA, A, BBB, BB, B } and V = { BBB,BB, B, CCC, CC } . (a) Find the intersection W and V. (b) Describe the union W or V. (c) Find the complement ( W or V ) c .