The probability thatapresident of the United States attends Harvard is about 18%.The odds that a president is affiliated with the Democratic Party is roughly 36%. The probability that a president both attends Harvard and is a democrat isabout 7%. (Harvard=H,Decomcratic=D) a.What percentage ofpresidents do NOT attend Harvard NOR affiliate with thedemocratic party? b.Are H and Dmutually exclusive events? Why or why not? c. Are the two events, H and D, independent? Explain, using probabilities. d.If we knowa president is affiliated with the Democraticparty, what is the probability that they attended Harvard? Solution a) P(H U D)\' = 1 - P(H U D) = 1 - [P(H) + P(D) - P(H n D)] = 1 - (0.18+0.36-0.07) = 0.53 [answer] ********************* b) As P(H n D) =/= 0 but rather is 0.07, then they are no mutually exclusive. [NO] ********************* c) If they are independent, P(H) = P(H|D) As P(H|D) = P(H n D)/P(D) = 0.07/0.36 = 0.194444444 P(H) = 0.18 As they are not equal (although close), they are not independent. ******************** d) P(H|D) = P(H|D) = P(H n D)/P(D) = 0.07/0.36 = 0.194444444 [ANSWER].