9. Suppose that the probability that an incoming email is a spam is p(S), that t

Question

9. Suppose that the probability that an incoming email is a spam is p(S), that the probability that the word w occurs in the subject line ofthe spam is p(w), and that q(w) is the probability that the word w occurs in the subject line of an email that is not a spam. What is the probability that an incoming email containing the word w is spam?

10. Suppose the rule for lottery is the following: Each lottery ticket is $1, on which a buyer chooses 6 numbers from {1, 2,3, ...,50} with repetitions allowed to form an ordered list of6 numbers. Ifa ticket's 6 numbers match the six winning numbers in the right order, the buyer wins exactly $10 million, otherwise the buyer wins nothing. Suppose that when a buyer chooses the 6 numbers for a ticket, each number from { I, 2,3, ..., 50) is equally likely to be chosen. Under this rule, what is the expected value of the amount of money a ticket buyer can win?

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