Problem 3. A study of male criminals in Philadelphia found that the probability that one type of offense is followed by another type can be described by the following transition table: Current Nonindex Injury Theft Damage Combination Next Nonindex Injury Theft Damage Combination 0.645 0.099 0.152 0.033 0.071 0.611 0.090 0.514 0.118 0.609 0.042 0.523 0.179 0.138 0.128 0.033 0.067 0.271 0.030 0.107 0.178 0.064 0.093 0.183 0.022 (a) For a criminal who commits theft, what is the probability that his next crime is also a theft? (b) For a criminal who commits theft, what is the probability that his second crime after that is also a theft? (c) If this trends continue, what are the long-term probabilities for each type of crime?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Problem 3. A study of male criminals in Philadelphia found that the probability
that one type of offense is followed by another type can be described by the following
transition table:
Current
Nonindex
Injury
Theft
Damage
Combination
Next
Nonindex Injury Theft Damage
0.645
0.099 0.152 0.033
0.611
0.514
0.609
0.523
0.138 0.128 0.033
0.067 0.271
0.030
0.107 0.178
0.093 0.183
0.064
0.022
Combination
0.071
0.090
0.118
0.042
0.179
(a) For a criminal who commits theft, what is the probability that his next crime is
also a theft?
(b) For a criminal who commits theft, what is the probability that his second crime
after that is also a theft?
(c) If this trends continue, what are the long-term probabilities for each type of crime?
Transcribed Image Text:Problem 3. A study of male criminals in Philadelphia found that the probability that one type of offense is followed by another type can be described by the following transition table: Current Nonindex Injury Theft Damage Combination Next Nonindex Injury Theft Damage 0.645 0.099 0.152 0.033 0.611 0.514 0.609 0.523 0.138 0.128 0.033 0.067 0.271 0.030 0.107 0.178 0.093 0.183 0.064 0.022 Combination 0.071 0.090 0.118 0.042 0.179 (a) For a criminal who commits theft, what is the probability that his next crime is also a theft? (b) For a criminal who commits theft, what is the probability that his second crime after that is also a theft? (c) If this trends continue, what are the long-term probabilities for each type of crime?
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