A hotel asked its customers to rate their stays as Excellent, Good, Fair, or Poo
ID: 3271574 • Letter: A
Question
A hotel asked its customers to rate their stays as Excellent, Good, Fair, or Poor. The following table shows the frequency of each rating as well as the gender of the customer. Determine the probability that a randomly selected customer. a. Rated his or her stay as Excellent b. Rated his or her stay as either Good or Fair c. Rated his or her stay as other than Poor d. Was a man who rated his stay as Good e. Either was a woman or rated his or her stay as Fair f. Rated her stay as Good, given the customer was a woman g. Was a woman, given the person rated the stay as Poor h. Construct a decision tree for these events.Explanation / Answer
Rating Men Women Total
Excellent 3 9 12
Good 20 12 32
Fair 16 7 23
Poor 6 2 8
Total 45 30 75
(a) P(Excellent) = 12/75 = 0.16
(b) P(Good OR Fair) = P(Good) + P(Fair) = 32/75 + 23/75 = 0.4267 + 0.3067 = 0.7334
(c) P(other than Poor) = 1 - P(Poor) =1 - 8/75 = 1 - 0.1067 = 0.8933
(d) P(Man & Good) = 20/75 = 0.2667
(e) P(Woman OR Fair) = P(Woman) + P(Fair) - P(Woman & Fair) = 30/75 +23/75 - 7/75 = 0.4 + 0.3067 - 0.0933 = 0.6134
(f) = P(Good/Woman) = P(Good & Woman)/P(Woman) = (12/75)/(30/75)=0.16/0.4=0.4
(g) P(Woman/Poor)=P(Woman & Poor)/P(Poor) = (2/75)/(8/75)=0.0267/0.1067=0.2502
FIRST 7 QUESTIONS ANSWERED AS PER DIRECTIONS FOR ANSWERING.
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