The probability that a president of the United States attend

The probability that a president 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 is about 7%. (Harvard=H, Decomcratic=D)

a. What percentage of presidents do NOT attend Harvard NOR affiliate with the democratic party?

            b. Are H and D mutually exclusive events? Why or why not?

            c. Are the two events, H and D, independent? Explain, using probabilities.

d. If we know a president is affiliated with the Democratic party, what is the probability that they attended Harvard?

Solution

a) percentage of presidents do NOT attend Harvard NOR affiliate with the democratic party = 100 - (18 + 36 - 7)

                                                                                                                                                  = 53 %

b) No, H and D are not mutually exclusive events. Because P(H and D) is not equals to zero, it is equals to 0.07.

c) P(H) = 0.18

P(D) = 0.36

P(H and D) = 0.07

P(H) * P(D) = 0.0648

since P(H and D) not equals to P(H) * P(D), so they are not independent

d) P(H|D) = P(H and D) / P(D)

                = 0.07 / 0.36

                =.1944 (ANS)