1. [-/8.5 Points] DETAILS MY NOTES PRACTICE ANOTHER To better understand how husbands and wives feel about their finances, a magazine conducted a national poll of 1,007 married adults age 25 and older with household incomes of $50,000 or more. The following table shows the couples' responses to the question "Who is better at getting deals?" Who Is Better? Respondent I Am My Spouse We Are Equal Husband 278 125 101 Wife 289 113 101 (a) Develop a joint probability table and use it to answer the following questions. (Round your answers to four decimal places.) Response Totals I am My Spouse We Are Equal Husband Spouse Wife Totals (b) According to the marginal probabilities, what is the most likely response? I am O my spouse O we are equal (c) Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? (Round your answer to four decimal places.) (d) Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband? (Round your answer to four decimal places.) (e) Given a response "My spouse" is better at getting deals, what is the probability that the response came from a husband? (Round your answer to four decimal places.) (f) Given a response "We are equal," what is the probability that the response came from a husband? What is the probability that the response came from a wife? 2. [-/2.75 Points] DETAILS The prior probabilities for events A and A are P(A) = 0.40 and P(A2) = 0.60. It is also known that P(An A2) = 0. Suppose P(B | A) = 0.20 and P(B | A2) = 0.05. (a) Are A and A2 mutually exclusive? They -Select- mutually exclusive. How could you tell whether or not they are mutually exclusive? O P(A) + P(A | A2) # O P(A2) + P(A2 | A) P(An A) = 0 P(A) + P(A2) = 1 O P(B | A) + P(B | A2) (b) Find P(An B) and P(A2 n B). (Give your answers to two decimals.) P(An B) = P(An B) = (c) Find P(B). Give your answer to two decimals. P(B) = (d) Find P(A | B) and P(A2 | B). (Round your answers to four decimal places.) 1 P(A | B) = P(A2 B) Tutorial 3. [-/1.5 Points] DETAILS MY NOTES PRACTICE ANOTHER A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 3% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a probability of 0.03 that any particular cardholder will default. The bank also found that the probability of missing a monthly payment is 0.24 for customers who do not default. Of course, the probability of missing a monthly payment for those who default is 1. (a) Given that a customer misses a monthly payment, compute the probability that the customer will default. (Round your answer to 2 decimal places.) (b) The bank plans to recall its card from customers who miss a monthly payment, if the probability those customers will default is greater than 0.20. Should the bank recall its card from a customer who has missed a monthly payment? Why or why not? The bank ---Select--- recall its card because the probability of default for these customers is --Select--- than 0.20. 4. [-/7.25 Points] DETAILS Preliminary studies determined the following probabilities for finding different qualities of oil on land owned by an Alaskan oil company: P(high-quality oil) = 0.50 P(medium-quality oil) = 0.30 P(no oil) 0.20 (a) What is the probability of finding oil? P(Oil) = (b) After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test, given the quality of oil in the well, are known to be: P(soil | high-quality oil) = 0.30 P(soil | medium-quality oil) = 0.80 P(soil | no oil) = 0.20 Complete the table below by finding the indicated probabilities. (Round your answers to two decimal places.) Events P(A) P(S|A,) High Quality (A1) 0.50 0.30 Medium Quality (A2) 0.30 0.80 No Oil (A3) 0.20 0.20 Total 1.00 P(S) P(A,S) P(A,S) 1.00 Find the probability of finding oil after the particular type of soil is detected. (Round your answer to two decimal places.) P(oil | S) = If the test indicates that the particular type of soil is present, is the company more likely or less likely to find oil? more likely less likely Given the test indicates the particular soil type is present, which oil type is more likely to be found? medium quality oil high quality oil