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EXAMPLE 1 Máňufacturing 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

EXAMPLE 1 Máňufacturing 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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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could you please explain me the 0.85, how it was calculated? 

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
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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