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Brand A light bulbs have exponential life times, with mean 1 year. Brand B light bulbs have exponential life times, with mean 2 years. They look the same. I have two brand A bulbs and one brand B bulb in a box (and I don't know which is the brand B bulb). I choose a bulb at random and screw it into a socket. Let T be the number of years it takes for the chosen bulb to burn out. Let "A" be the event that I picked a brand A bulb and "B" be the event that I picked the B bulb. (a). Find P( T > 4 ). (b). Find P( B | T > 4 ). (c). Find P ( T > 6 | T > 4 )

Brand A light bulbs have exponential life times, with mean 1 year. Brand B light bulbs have exponential life times, with mean 2 years. They look the same. I have two brand A bulbs and one brand B bulb in a box (and I don't know which is the brand B bulb). I choose a bulb at random and screw it into a socket. Let T be the number of years it takes for the chosen bulb to burn out. Let "A" be the event that I picked a brand A bulb and "B" be the event that I picked the B bulb. (a). Find P( T > 4 ). (b). Find P( B | T > 4 ). (c). Find P ( T > 6 | T > 4 )

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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Brand A light bulbs have exponential life times, with mean 1 year. Brand B light bulbs have exponential life times, with mean 2 years. They look the same. I have two brand A bulbs and one brand B bulb in a box (and I don't know which is the brand B bulb). I choose a bulb at random and screw it into a socket. Let T be the number of years it takes for the chosen bulb to burn out. Let "A" be the event that I picked a brand A bulb and "B" be the event that I picked the B bulb. (a). Find P( T > 4 ). (b). Find P( B | T > 4 ). (c). Find P ( T > 6 | T > 4 )..
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