52% about 5 out of 10 strongly oppose the casio. Complete parts a According to a

Question

52% about 5 out of 10 strongly oppose the casio. Complete parts a According to a survey 52% of the residents of a city oppose a downtown casino. Of these hrough (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 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 randomiy selected resident to oppose the casino and strongly oppose the casino? Explain. Choose the correct answer below O A. Yes, this is unusual because the probability is not less than or equal to 0.05 O B. No, this is not unusual because the probability is not less than or equal to 0.05 C. No, this is not unusual because the probability is less than or equal to 005 O D. Yes, this is unusual because the probability is less than or equal to 0.05 Glick to select your answerts).

Explanation / Answer

Let us denote

A := { a random resident of city opposes downtown casino }

B := { a random resident of city strongly opposes downtown casino }

So given

P (A)= 0.52 ; P(B|A) = 0.5

(a)   To find P (AB) .

Multiplication theorem of probability states

P (AB) = P(A)* P(B|A) provided P(A) >0

i.e. P (AB)= 0.52* 0.5 = 0.26

    (b)     To find P(Bc |A).

                We have

                P(B |A) + P(Bc |A) =1

                i.e. P(Bc |A) = 1- P(B |A) = 1- 0.5 = 0.5

(c)

P ( A randomly selected resident of city opposes downtown casino and strongly opposes the casino)

= P (AB) =0.26    > 0.05 , (from part (a))

Thus option ‘B’ is correct.

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