In a certain small town, 3 professional burglars are currently out of prison: Alex, Becky, and Carl. Alex has in the past committed 55% of the burglaries committed by the three, Becky  31%, and Carl the rest. But only 1/3 of Alex’s jobs are burglaries of a residence, while half of Becky’s are, and all of Carl’s are. a) What is the probability that the next burglary in town (if one of the three did it) is the burglary of a residence? b) Sure enough, a resident reports a home burglary. If one of the three did it, what is the probability Becky was guilty

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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In a certain small town, 3 professional burglars are currently out of prison: Alex, Becky, and Carl. Alex has in the past committed 55% of the burglaries committed by the three, Becky 
31%, and Carl the rest. But only 1/3 of Alex’s jobs are burglaries of a residence, while half of Becky’s are, and all of Carl’s are.
a) What is the probability that the next burglary in town (if one of the three did it) is the burglary of a residence?
b) Sure enough, a resident reports a home burglary. If one of the three did it, what is the probability Becky was guilty

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