B) An insurance company believes that people can be divided intotwo categories; those who are accident prone and those who are not.The company’s statistics show that an accident-prone person willhave a car accident within a one-year period with probability 0.4,whereas this probability decreases to 0.2 for a person who is notaccident prone. The data also suggest that 30% of the population isaccident prone. What is the probability that a new policyholderwill have an accident within a year of purchasing the policy?
B)A spam filter is designed by looking at commonly occurringphrases in spam. Suppose that
80% of all emails sent are spam. In 10% of the spam emails, thephrase "free money" is used,
whereas this phrase is only used in 1% of non-spam emails. A newemail has just arrived, which
does mention "free money". What is the probability that it isspam?
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