A survey was conducted among 1000 people on their opinion about President Obama\

Question

A survey was conducted among 1000 people on their opinion about President Obama's health care proposal. The following information was collected: There were 600 Democrats and 400 Republicans Among the Democrats, 500 supported the President's health care proposal and the rest didn't. Among the Republicans, 200 supported the President's health care proposal and the rest didn't. Answer the following questions: Suppose a person is selected randomly from these 1000 people What is the probability that the person is a Republican? What is the probability that the person is a Democrat who doesn't support the President's proposal? What is the probability that the person is a Democrat or the person supports the President's proposal? What is the probability that the person supports the President's proposal knowing that the person is a Republican? Are "being a Republican" and "supporting the President's proposal" independent events? Are "being a Republican" and "supporting the President's proposal" mutually exclusive events'?

Explanation / Answer

Consider:

i.

From the table,

P(R) = 400/1000 = 0.4 [ANSWER]

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ii.

From the table,

P(D n S') = 100/1000 = 0.1 [ANSWER]

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iii.

From the table,

P(D U S') = (500+100+200)/1000 = 0.8 [ANSWER]

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iv.

from the table,

P(S|R) = 200/400 = 0.5 [ANSWER]

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v.

As from the table,

P(S) = 700/1000 = 0.7

and P(S|R) = 0.5, thus,

P(S) =/= P(S|R), then NO, THEY ARE NOT INDEPENDENT. [ANSWER]

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vi.

As from the table,

P(R n S) = 200/1000 =/= 0, then NO, THEY AR ENOT MUTUALLY EXCLUSIVE. [ANSWER]

Democrats Republicans Total Support 500 200 700 Not Support 100 200 300 Total 600 400 1000

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