An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each ofthe three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of thethree factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman hasall three risk factors, given that she has A and B, is 1/3 .What is the probability that a woman has none of the three risk factors, given that she does not have risk factor A?A) 0.280B) 0.311C) 0.467D) 0.484E) 0.700

We want to find the probability that a woman has none of the three risk factors (denoted as ~A)…

Answered: An actuary is studying the prevalence…

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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12. An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3. Calculate the probability that a woman has none of the three risk factors, given that she does not have risk factor A. (A) 0.280 (B) 0.311 (C) 0.467 (D) 0.484 (E) 0.700 4
A blood bank asserts that a person with type O blood and a negative Rh factor (Rh−) can donate blood to any person with any blood type. Their data show that 49% of people have type O blood and 17% of people have Rh− factor; 52% of people have type O or Rh− factor. A. Find the probability that a person has both type O blood and the Rh− factor. B. Find the probability that a person does NOT have both type O blood and the Rh− factor.
TABLE 4.6 Sneakers are no longer just for the young. In fact, most adults own multiple pairs of sneakers. Table 4.6 gives the fraction of U.S. adults 20 years of age and older who own five or more pairs of wearable sneakers, along with the fraction of the U.S. adult population 20 years or older in each of five age groups. Use the Law of Total Prob- ability to determine the unconditional probability of an adult 20 years and older own- ing five or more pairs of wearable sneakers. 6 Probability Table Groups and Ages G3 35-49 Fraction with ≥ 5 Pairs .13 Fraction of U.S. Adults 20 and Older .30 G₁ 20-24 26 .09 G₂ 25-34 .20 .18 G4 50-64 18 .25 G5 ≥ 65 .14 .18 AI
There are three modes of transporting material from Boston to Houston: by land (either by highway or railway), seaor air. Half of the materials are transported by land20% by sea, and the rest by air. Also, 60% of all land transportation is by highway and the rest is by rail shipments.Cargo traveling by each mode of transportation has a different probability of being damaged during shipment. The percentages of damaged cargo are as follows: 12% by highway, 3% by rail, 5% by seaand 2% by airIf a damaged cargo is received, what is the probability that it was shipped by sea?
The blood-typing system is based on the presence or absence of antigens. A person with antigen A has blood type A. A person with antigen B has blood type B, and a person with both antigens has the blood type AB. If there are no antigens, then the blood type is O. In addition, blood types are also identified as Rh-positive or Rh-negative based on a different antigen. What is the probability that a person has the A antigen or is Rh-positive?
A manufacturer of tablet ipods is concerned about the possible recall of their best-selling model. If there was a recall, there is a 0.30 probability that a defect is in the videocard, 0.20 in the audiocard, 0.18 in the memory card, and 0.45 in ww w some other areas. What is the probability that the defect is the videocard or the memory card if the probability of ww m m defects in both parts simultaneously is 0.20?
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
In a marketing research survey, people are interviewed about product usage. One of the questions is about the brand of toothpaste used. If it is known that 14% of the population use brand A and 9% use brand B, what is the probability that a randomly chosen person will be a user of one of the two brands? (Assume that only one brand is used at a given time).
section 5.5 A personnel director has two lists of applicants for jobs. List 1 contains names of 24 women and 8 men, whereas List 2 contains the names of 9 women and 16 men. A name is randomly selected from List 1 and added to List 2. A name is then randomly selected from the augmented List 2. Given that the name selected is that of a man, what is the probability that a woman's name was originally selected from List 1? Round your answer to four decimal places, if necessary.
We randomly select a batch of 40 computer disks for shipment. The probability of selecting a good disk is the same as the probability of selecting a defective disk. In part C, you will determine the probability that this shipment contains 10 defective disks and 30 good disks for our batch or 15 defective disks and 25 good disks for our batch. Note: I am not asking for an example of an outcome, although I may ask for examples of outcomes on the exam. A. What is the size of your sample space S? i.e., How many different outcomes (batches of 40 disks) in your sample space? What are the conditions? What counting technique(s) are you using? B. How many outcomes when randomly selecting 10 defective disks and 30 good disks for our batch or 15 defective disks and 25 good disks for our batch. What are the conditions? What counting technique(s) are you using? C What is the probability of randomly selecting a batch of 10 defective disks and 30 good disks or a batch of 15 defective disks and 25…
From experience, a wheat farmer living in Manitoba, Canada finds that his annual profit (in Canadian dollars) is $80,000 if the summer weather is typical, $50,000 if the weather is unusually dry, and $20,000 if there is a severe storm that destroys much of his crop. Weather bureau records indicate that the probability is 0.70 of typical weather, 0.20 of unusually dry weather, and 0.10 of a severe storm. Let X denote the farmer's profit next year (a) Construct a table with the probability distribution of X. (b) What is the probability that the profit is $50,000 or less? (c) Find the mean of the probability distribution of X. Interpret. (d) Suppose the farmer buys insurance for $3000 that pays him $20,000 in the event of a severe storm that destroys much of the crop and pays nothing otherwise. Find the probability distribution of his profit. Find the mean and summarize the effect of buying this insurance.
According to the Center for Disease Control and Prevention (CDC), up to 20% of Americans contract the influenza virus each year, and approximately 3% of all births in the United States result in birth defects each year. Consider two randomly selected Americans and assume that these two randomly selected Americans are independent of each other. The probability that neither of these two randomly selected Americans will contract the influenza virus in a given year is

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