1. An insurance company classifies its policyholders into three categories: low risk, mediumrisk and high risk. The chance that a policyholder classified as low risk, medim risk, andhigh risk will be involved in an accident within the following year is 0.05, 0.10 and 0.20,respectively. If 50% of the policies are low risk, 35% are medium risk and 15% are highrisk, what is the chance that a random policyholder will experience an accident within theyear? At the end of the year, what is the probability that a policyholder is classified highrisk given that he or she experienced an accident within that year?

Let us define some events A : a policy holder is at low risk. B : a policy holder is at medium…

Answered: . An insurance company classifies its…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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6. Historically, a given day at the beginning of March in upstate New York has a 18% chance of snow and a 12% chance of rain. If there is a 4% chance it will rain and snow on a day, then which of the following represents the probability that a day in early March would have either rain or snow? (1) 0.30 (3) 0.02 (2) 0.34 (4) 0.26
7. Aaron purchased 19 video games. The defect rate for these types of video games is 1.8%. What is the probability that at least three of the video games he purchased are defective?
A bank recently discovered that approximately 1.6% of all commercial loans issued by the bank become delinquent. Norah, the bank's vice president of operations, is stunned by this discovery. In order to be prepared for the next board meeting, she investigates the matter by randomly selecting 554 commercial loans from the bank’s database and reviewing each loan. What is the probability that at least 12 of the loans in the sample are delinquent? Use Excel to find the probability. Round your answer to four decimal places.
If our goal was to play roulette so that we can "win it big". What does the expected value of a bet tell us about our chances of winning a large amount of money?
Addiction Medicine. The report “Addiction Medicine: Closing the Gap between Science and Practice” from the National Center on Addiction and Substance Abuse at Columbia University reveals that addiction treatment is neglected by the medical system in the United States. It shows, in particular, that 16% of Americans have the disease of addiction and that 90% of them receive no form of treatment. Determine the probability that a randomly selected American has the disease of addiction and receives no form of treatment. Interpret your answer in terms of percentages.
1. What are complementary events? 2. If the subjective probability that it will rain is 45%, what is the probability that it will not rain?
A study is conducted to assess the impact of caffeine consumption, smoking, alcohol consumption, and physical activity on cardiovascular disease. Suppose that 40% of participants consume caffeine and smoke. If eight participants are evaluated, what is the probability that: At most, six participants consume caffeine and smoke?
1. Researchers are interested in the relationship between vaping and upper respiratory infections. Suppose that 15% of their population of interest has vaped in the past year and 25% have had an upper respiratory infection in the past year. In addition, they know that 10% have both vaped and had an upper respiratory infection in the past year. What percent of the population has neither vaped nor had an upper respiratory infection in the past year? b. What is the probability of having an upper respiratory infection in the past year given that the person has vaped in the past year? What is the complement of the event in part b)? Be sure to interpret this probability in the context of the problem. a. C. d. What is the probability of having an upper respiratory infection in the past year given that the person has not vaped in the past year? Are the two events independent? Be sure to justify your answer. Based on your calculations what can you conclude about the relationship between vaping…
10. A bank classifies borrowers as high risk or low risk. Only 15% of its loans are made to those in the high-risk category. Of all its loans, 5% are in default, and 40% of those in default were made to high-risk borrowers. What is the probability that a high-risk borrower will default?
5. Five hundred tickets will be sold and these will be raffled during the town fiesta. One of these tickets will win ₱3000 and the rest will win nothing. What will be the expected outcome and variance of your gain if you will buy one of the tickets?6. Astrid tosses an unbiased coin. On each toss, she wins ₱50 if a head appears, and loses ₱40 if a tail appears. What will be the expected value and variance of her gain?
6. An actuary studying the insurance preferences of automobile owners makes the following conclusions: (i) An automobile owner is twice as likely to purchase collision coverage as disability coverage. (ii) The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage. (iii) The probability that an automobile owner purchases both collision and disability coverages is 0.15. (a)Calculate the probability that an automobile owner purchases neither collision nor disability coverage. (b) Calculate the probability that an automobile owner purchases only collision coverage.
3. Twenty five percent of a town's voters favor letting a major discount store move into their neighbourhood, 60% are against it and 15% are indifferent. What is the probability that a randomly selected voter from this town will either be against it or be indifferent?

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