Suppose an insurance company has three types of customers-high risk, medium risk and low risk. From the company's historical consumer database, it is known that 25% of its customers are high risk, 25% are medium risk, and 50% are low risk. Also, the database shows that the probability that a customer has at least one speeding ticket in one year is 0.25 for high risk, 0.16 for medium risk, and 0.10 for low risk. Now suppose a new customer wants to be insured and reports that he has had one speeding ticket this year. What is the probability that he is a high risk customer, given that he has had one speeding ticket this year?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Suppose an insurance company has three types of customers-high risk, medium
risk and low risk. From the company's historical consumer database, it is
known that 25% of its customers are high risk, 25% are medium risk, and 50%
are low risk. Also, the database shows that the probability that a customer has
at least one speeding ticket in one year is 0.25 for high risk, 0.16 for medium
risk, and 0.10 for low risk.
Now suppose a new customer wants to be insured and reports that he has had
one speeding ticket this year. What is the probability that he is a high risk
customer, given that he has had one speeding ticket this year?
Transcribed Image Text:Suppose an insurance company has three types of customers-high risk, medium risk and low risk. From the company's historical consumer database, it is known that 25% of its customers are high risk, 25% are medium risk, and 50% are low risk. Also, the database shows that the probability that a customer has at least one speeding ticket in one year is 0.25 for high risk, 0.16 for medium risk, and 0.10 for low risk. Now suppose a new customer wants to be insured and reports that he has had one speeding ticket this year. What is the probability that he is a high risk customer, given that he has had one speeding ticket this year?
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