A survey was conducted among 2000 people on their opinion ab

A survey was conducted among 2000 people on their opinion about President Obama\'s health care proposal. The following information was collected: There were 1200 Democrats and 800 Republicans Among the Democrats, 1000 supported the President\'s health care proposal and the rest didn\'t. Among the Republicans, 400 supported the President\'s health care proposal and the rest didn\'t. Answer the following questions: Suppose a person is selected randomly from these 2000 people What is the probability that the person is a Democrat? What is the probability that the person is a Republican who supports the President\'s proposal? What is the probability that the person is a Republican or the person does not support the President\'s proposal? What is the probability that the person does not support the President\'s proposal knowing that the person is a Democrat? Are \"being a Democrat\" and \"supporting the President\'s proposal\" independent events Are \"being a Democrat\" and \"supporting the President\'s proposal\" mutually exclusive events?

Solution

Let

D = democrat
R = republican
S = support

i)

P(D) = 1200/2000 = 0.6 [ANSWER]

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ii)

P(R n S) = 400/2000 = 0.2 [ANSWER]

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iii)

P(R U S\') = (800 + (1200-1000))/2000 = 0.5 [ANSWER]

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iv)

P(S\'|D) = 200/1200 = 0.166666667 [ANSWER]

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v)

Here,

P(S\') = ((1200-1000)+(800-400))/2000 = 0.3

As P(S\') =/= P(S\'|D), THEY ARE NOT INDEPENDENT.

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vi)

As some democrats support the president\'s proposal, then THEY ARE NOT MUTUALLY EXCLUSIVE EVENTS. [ANSWER]