
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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could you please explain me the 0.85, how it was calculated?

Transcribed Image Text:EXAMPLE 1
Manufacturing
A factory of the Global Manufacturing Company was manufacturing products with a
defect rate of 15% (based on data from the Harvard Business Review). If a customer pur-
chases 12 of the products, what is the probability of getting at least one that is defective?
SOLUTION
Step 1: Let A
= at least 1 of the 12 products is defective.
Step 2: Identify the event that is the complement of A.
A
= not getting at least 1 defect among the 12 items
= all 12 items are good with no defects
Step 3: Find the probability of the complement by evaluating P(A).
P(A) = P(all 12 items are good)
= 0.85 · 0.85•0.85 · 0.85 · 0.85 · 0.85 · 0.85 · 0.85 · 0.85•0.85 · 0.85 •0.85
= 0.8512
0.142
%3D
Step 4: Find P(A) by evaluating 1 – P(A).
P(A) = 1 – P(A) = 1 – 0.142
= 0.858
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