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)

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]