The probability that a president of the United States atten ds Harvard is about
ID: 3376839 • 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)
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]
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b)
As
P(H n D) =/= 0
but rather is 0.07, then they are no mutually exclusive. [NO]
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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.
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d)
P(H|D) = P(H|D) = P(H n D)/P(D) = 0.07/0.36 = 0.194444444 [ANSWER]
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