31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40. a. What is P(A n B)? b. What is P(A|B)? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer. d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem? 37. Giving Up Electronics. A 2018 Pew Research Center survey found that more Americans believe they could give up their televisions than could give up their cell phones (Pew Research website). Assume that the following table represents the joint probabilities of Americans who could give up their television or cell phone. Could Give Up Television Yes No Could Give Up Cellphone Yes .31 .17 .48 No .38 .14 .52 .69 .31 a. What is the probability that a person could give up her cell phone? b. What is the probability that a person who could give up her cell phone could also give up television? c. What is the probability that a person who could not give up her cell phone could give up television? d. Is the probability a person could give up television higher if the person could not give up a cell phone or if the person could give up a cell phone?