According to a survey, 59% of the residents of a city oppose a downtown casino.

Question

According to a survey, 59% of the residents of a city oppose a downtown casino. Of these 59% about 7 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 (a) The probability that a randomly selected resident opposes the casino and strongly opposes the casino is .

Explanation / Answer

Let A = oppose casino, B = strongly oppose casino.
Let A' and B' be the complementary events.

We're given P(A) = .59, P(B|A) = .7

a) P(A and B) = P(B|A)*P(A)

= .59 * .7 = .413

b) P(B' | A) = 1 - P(B|A) = 1 - .7 = .3.

An alternative way:

P(B' | A) = P(B'A)/P(A) = (P(A) - P(A and B))/ P(A) =

= (.59 - .413) / .59 = .3, using law of total probability in the numerator

c) it will not be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino

because 41.3% of residents fall in to that category.

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