110 47. Suppose A and B are two events with P(A) = 0.36, P(B) = 0.48, and the P(A or B) = 0.60. %3D %3D (a) Find P(An B). (b) Find P(A|B). (c) Are A and B independent events? Explain why or why not using probabilities. (d) Are A and B disjoint events? Explain why or why not using probabilities. 48. Can two events A and B be independent of one another and disjoint? Explain what conditions are needed for this to happen. 49. It is estimated that 63% of Americans will watch the Masters golf tournament and only 48% will watch the British Open. Of those who watch the British Open, 78% watched the Masters (a) Using M to denote the event "Watch the Masters" and B to denote the event "Watch the British Open", describe the probabilities given in the problem. (b) What is the probability that a randomly selected American watches both the Masters and the British Open? (c) What is the probability that a person watches the British Open if it is known that they watched the Masters tournament? (d) What is the probability that a person does not watch the British Open? (e) Are watching the Masters and watching the British Open independent events? Explain using probabilities. (f) Are watching the Masters and watching the British Open disjoint events? Explain using probabilities. 50. Explain the difference between independent events and disjoint events using probabilities and simple examples. 51. The Pew Research Center finds that the demographic make-up of political parties is changing drastically through the election cycles. Consider the following summary of education levels among party lines. Democrat Republican Total 68 31 College Degree No College Degree Total 37 132 69 63 200 100 100 (a) What is the probability a randomly selected participant has a college degree? (b) What is the probability that a randomly selected participant is a democrat? (c) What is the probability that a randomly selected participant is a democrat and has a college degree? (d) Of those who have college degrees, what is the probability of being a democrat? (e) What is the probability of begin a democrat or having a college degree? (f) Are having a college degree and being a democrat disjoint events? (g) Are having a college degree and being a democrat independent events?

States Infection Recovery Total A 169 158   B ) 259 380   C ( 0 78   Total     N= a. recovered given that he is from state C  b. from state B given that he is infected.

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Showing the details, calculate the following expressions or give reason why they are not defined, when A = 3 1 -3 1 -3 4 2 2 5 u= 2 0 -5 0 B = -4 V = -3 3 4 0-2 2 0