A certain article manufactured in our facilities may present three different types of defects: minor aesthetic, major aesthetic and functional. Of the last 650 manufactured items, 69 have a minor cosmetic defect, 26 have a major cosmetic defect and 17 have a functional defect
Only 4 of the 650 present the three types of defect, while 101 present at least one of the aesthetic defects. Thirteen articles with major cosmetic defect and functional defect were identified, while there were 6 articles with minor cosmetic defect and functional defect.
Calculate the probability of:
a) Randomly select an item without defect
b) The probability of selecting an item with both types of
aesthetic defects
c) If you select an item and it turns out to have a minor cosmetic
defect, what is the probability that it also has a functional
defect?
Answer:
Let A, B and C denote the number of items with Minor aesthetic, Major aesthetic and Functional defects respectively
n = 650
n(A) = 69, n(B) = 26, n(C) = 17,
n(A and B and C) = 4
n(A or B or C) = 101
n(B and C) = 13
n(A and C) = 6
(a) The required probability = 1 - P(A or B or C)
= 1 - 101/650 = 0.845
(b) n(A and B) = n(A or B or C) - n(A and B and C) - n(A) - n(B) - n(C) + n(B and C) + n(A and C)
= 101 - 4 - 69 - 26 - 17+ 13 + 6 = 4
The required probability = 6/650 = 0.009
(c) The required probability = P(C | A) = P(A and C)/P(A)
= 6/69 = 0.0869
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