According to a survey, 51% of the residents of a city oppose a downtown casino.

Question

According to a survey, 51% of the residents of a city oppose a downtown casino. Of these 51% about 8 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.

Answer:
(a) The probability that a randomly selected resident opposes the casino and strongly opposes the casino is _.

(Round to three decimal places as needed.)

(b) The probability that a randomly selected resident who opposes the casino does not strongly opposes the casino is _.

(Round to three decimal places as needed.)

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

A. No, this is not unusual because the probability is less than or equal to 0.05.

B. Yes, this is unusual because the probability is not less than or equal to 0.05.

C. No, this is not unusual because the probability is not less than or equal to 0.05.

D. Yes, this is unusual because the probability is less than or equal to 0.05.

Explanation / Answer

Solution :

?(a) The probability that a randomly selected resident opposes the casino and strongly opposes the casino is (8/10)*0.51

=> 0.408

?(b) The probability that a randomly selected resident who opposes the casino does not strongly opposes the casino is (1 - (8/10))*0.51

=> 0.102

(c) Option C. ?No, this is not unusual because the probability is not less than or equal to 0.05.

Because , P(oppose the casino and strongly opposes the casino) = 0.408 > 0.05 and hence it is not unusual for a randomly selected resident to oppose the casino and strongly oppose the casino

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