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. Consider the following example set of responses to the question "Who is better at getting deals?" Who Is Better? Respondent I Am My Spouse We Are Equal Husband 278 126 101 Wife 290 111 101 (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? O I am O my spouse we are equalv we ale equal (c) Given that the respondent is a husband, what is the probability that he feels he is betber at getting deals than his wife? (Round your answer to four decimal places.) :I (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.) :I (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.) :I (F) Given a response "We are equal." what is the probability that the response came from a husband? :I What is the probability that the rEponse came from a wife? :I A real estate company recently became interested in determining the likelihood of one of their listings being sold within a certain number of days. An analysis of company sales of 800 homes in previous years produced the following data. Days Listed Until Sold Total Under 30 31-90 Over 90 Under $150,000 10 50 40 100 Initial $150,000-$199,999 20 150 80 250 Asking Price $200,000-$250,000 280 100 20 100 Over $250,000 10 10 30 50 Total 320 310 170 800 (a) If A is defined as the event that a home is listed for more than 90 days before being sold, estimate the probability of A. (b) If B is defined as the event that the initial asking price is under $150,000, estimate the probability of B. (c) What is the probability of A n B? (d) Assuming that a contract was just signed to list a home with an initial asking price of less than $150,000, what is the probability that the home will take the company more than 90 days to sell? (e) Are events A and B independent? O Yes, because P(A | B)