Probability 05

Exercise

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Exercise

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Exercise

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Exercise

Ms. Aquina has just had a biopsy on a possibly cancerous tumor. Not wanting to spoil a weekend family event, she does not want to hear any bad news in the next few days. But if she tells the doctor to call only if the news is good, then if the doctor does not call, Ms. Aquina can conclude that the news is bad. So, being a student of probability, Ms. Aquina instructs the doctor to flip a coin. If it comes up heads, the doctor is to call if the news is good and not call if the news is bad. If the coin comes up tails, the doctor is not to call. In this way, even if the doctor doesn’t call, the news is not necessarily bad. Let be the probability that the tumor is cancerous; let be the conditional probability that the tumor is cancerous given that the doctor does not call.

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Exercise

Suppose that an insurance company classifies people into one of three classes: good risks, average risks, and bad risks. The company’s records indicate that the probabilities that good-, average-, and bad-risk persons will be involved in an accident over a 1-year span are, respectively, . If of the population is a good risk, an average risk, and a bad risk, what proportion of people have accidents in a fixed year? If policy holder A had no accidents in 1997, what is the probability that he or she is a good or average risk?

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