Question

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

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.

Math   Statistics-And-Probability   
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Answer #1

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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