1help with stat hw A table classifying a sample of 122 patro

A table classifying a sample of 122 patrons of a restaurant according to type of meal and their rating of the service is shown to the right. Suppose we select, at random, one of the 122 patrons. Complete parts a through c below. Given that the meal was dinner, what is the probability that the service was good? Given that the meal was dinner, the probability that the service was good is (Type an integer or decimal rounded to three decimal places as needed.) If the respondent gives a good rating, what is the probability that the respondent had lunch? If the respondent gives a good rating, the probability that the respondent had lunch is. (Type an integer or decimal rounded to three decimal places as needed.) Are the events {good service} and {dinner} independent? No, because P(good|dinner) notequalto P(good). Yes, because P(good|dinner) = P(good). Yes, because P(good|dinner) notequalto P(good). No, because P(good|dinner) = P(good).

Solution

a)

P(good|dinner) = 22/65 = 0.338461538 = 0.338 [answer]

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b)

P(lunch|good) = 40/62 = 0.64516129 = 0.645 [answer]

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c)

As

P(good|dinner) = 0.338
P(good) = 62/122 = 0.508196721

and they are not equal,

OPTION A: No, because P(good|dinner) =/= P(good). [ANSWER]