Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 84% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 32% of all defective components. What is the probability that the following occur? (a) A defective component will be detected only by the first inspector? 0.1344 × A defective component will be detected by exactly one of the two inspectors? 0.2688 × (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)? 0.032768
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 84% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 32% of all defective components. What is the probability that the following occur? (a) A defective component will be detected only by the first inspector? 0.1344 × A defective component will be detected by exactly one of the two inspectors? 0.2688 × (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)? 0.032768
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Transcribed Image Text:Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 84% of all defectives that are present, and the second inspector does likewise. At least
one inspector does not detect a defect on 32% of all defective components. What is the probability that the following occur?
(a) A defective component will be detected only by the first inspector?
0.1344
×
A defective component will be detected by exactly one of the two inspectors?
0.2688
×
(b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?
0.032768
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