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According to a survey, 57% of the residents of a city oppose a downtown casino,

ID: 3134782 • Letter: A

Question

According to a survey, 57% of the residents of a city oppose a downtown casino, Of these57% about 88 out of 10 strongly oppose the casino.Complete parts (a) through (c).

(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino.

(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino? Explain.

Explanation / Answer

Let

O = opposes
S = strongly opposes

a)

P(S n O) = P(O) P(S|O) = 0.57*(8/10) = 0.456 [ANSWER]

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b)

Note that

P(S'|O) = 1 - P(S|O)

hence,

P(S'|O) = 1 - (8/10) = 0.2 [ANSWER]

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c)

From a), the probability is 0.456, so IT IS NOT UNUSUAL. [ANSWER]

[Unusual events have probability less than 0.05.]

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