Flashner Marketing Research Inc. specializes in providing assessments of the prospects for women’s apparel shops in shopping malls. Al Flashner, president, reports that he assesses the prospects as good, fair, or poor. Records from previous assessments show that 60 percent of the time the prospects were rated as good, 30 percent of the time fair, and 10 percent of the time poor. Of those rated good, 80 percent made a profit the first year; of those rated fair, 60 percent made a profit the first year; and of those rated poor, 20 percent made a profit the first year. Connie’s Apparel was one of Flashner’s clients. Connie’s Apparel made a profit last year. What is the probability that it was given an original rating of poor?
step by step explanation this is probability and statistics question.
Answers
Given : reports that assesses the prospects as good, fair, or poor.
To find : probability that it was given an original rating of poor
Solution:
Rate good = 60 % = 0.6
and made profit = 80 % = 0.8
Hence Rate good and made profit = 0.6 * 0.8 = 0.48
Similarly
Rate fair and made profit = 0.3 * 0.6 = 0.18
Rated poor and made profit = 0.1 * 0.2 = 0.02
Total made profit = 0.48 + 0.18 + 0.02 = 0.68
Rated poor and made profit = 0.02
Probability that it was given an original rating of poor = 0.02/0.68
= 1/34
≈ 0.0294
≈ 2.94 %
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