The probability that a president of the United States attends Harvard is about 1
ID: 3441820 • Letter: T
Question
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?
Explanation / Answer
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)
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