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Unformatted text preview: P (Length too long) = 25 / 1000 40 / 1000 = 5 8 = 0 . 625 2. A factory has two machines that manufacture lightbulbs. The probability that a lightbulb comes from machine 1 is 45% and 55% of all lightbulbs come from machine 2. Machine 1 produces defects at a rate of 2% while machine 2 produces defects at a rate of 1%. What is the probability that a randomly selected lightbulb is from machine 1 given that it is defective? Answer: Let M 1 denote the lightbulb is from Machine 1, M 2 denote the lightbulb is from Machine 2 and D denote the lightbulb is defective. P ( M 1  D ) = P ( D  M 1 ) P ( M 1 ) P ( D  M 1 ) P ( M 1 ) + P ( D  M 2 ) P ( M 2 ) = (0 . 02)(0 . 45) (0 . 02)(0 . 45) + (0 . 01)(0 . 55) = 18 29 ≈ . 62...
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This note was uploaded on 12/13/2011 for the course STA 3032 taught by Professor Kyung during the Fall '08 term at University of Florida.
 Fall '08
 Kyung
 Statistics

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