A table classifying a sample of 106 patrons of a restaurant according to type of

Question

A table classifying a sample of 106 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 106 patrons. Complete parts a through c below. a. Given that the meal was lunch, what is the probability that the service was poor? Given that the meal was lunch, the probability that the service was poor is (Type an integer or decimal rounded to three decimal places as needed.) b. 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.) c. Are the events {poor service} and {lunch} independent? A. No, because P(poor|lunch) = P(poor). B. Yes, because P(poor|lunch) = P(poor). C. No, because P(poor|lunch) notequalto P(poor). D. Yes, because P(poor|lunch) notequalto P(poor).

Explanation / Answer

Answer to the questions below:

a. P( service was poor | meal was lunch) = 10/47

b. P( good rating | respondant had lunch) = 45/59

c. If, P(poor|lunch) = P(poor) then events are independent
= (10/56) = 47/106, since it is not equal,
we have NO. because P(poor|lunch) != P(poor)

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