Q3/ An insurance company considers that people can be split in two groups : thosewho are likely to have accidents and those who are not. Statisties show that a personwho is likely to have an accident has probability 0.4 to have one over a year; thisprobability is only 0.2 for a person who is not likely to have an accident. We assumethat 30% of the population is likely to have an accident.(a) What is the probability that a new customer has an accident over the first year ofhis contract?(b) A new customer has an accident during the first year of his contract. What is theprobability that he belongs to the group likely to have an accident?Ans: (a- 0.26, b- 0.46)

Let us define some events A : a new customer belongs to the group likely to have an accident. B : a…

Answered: (a) What is the probability that a new…

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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A survey found that 62% of callers in the United States complain about the service they receive from a call center if they suspect that the agent who handled the call is foreign.11 Given this context, what is the probability that (state your assumptions) (a) the next three consecutive callers complain about the service provided by a foreign agent? (b) the next two calls produce a complaint, but not the third? (c) two out of the next three calls produce a complaint? (d) none of the next 10 calls produces a complaint?
Peter oversees the electronics section of a large department store. He has noticed that the probability that a customer who is just browsing will buy something is 0.2. Suppose that 10 customers browse in the electronics section each hour. (i) What is the probability that no browsing customers will buy something during a specified hour? (ii) What is the probability that at least one browsing customer will buy something during a specified hour?
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An insurance company considers that people can be split in two groups : those who are likely to have accidents and those who are not. Statistics show that a person who is likely to have an accident has probability 0.4 to have one over a year; this probability is only 0.2 for a person who is not likely to have an accident. We assume that 30% of the population is likely to have an accident. (a) What is the probability that a new customer has an accident over the first year of his contract? (b) A new customer has an accident during the first year of his contract. What is the probability that he belongs to the group likely to have an accident? Ans: (a- 0.26, b- 0.46)
Suppose Nate wins 25% of all thumb wars. (a) What is the probability that Nate wins two thumb wars in a row? (b) What is the probability that Nate wins three thumb wars in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Nate wins three thumb wars in a row, but does not win four in a row. (a) The probability that Nate wins two thumb wars in a row is 0.0625 (Round to four decimal places as needed.) (b) The probability that Nate wins three thumb wars in a row is (Round to four decimal places as needed.) (c) The probability that Nate wins three thumb wars in a row, but does not win four in a row is (Round to four decimal places as needed.)
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Sneakers are no longer just for the young. In fact, most adults own multiple pairs of sneakers. Table gives the fraction of US adults 20 years of age and older who own five or more pairs of wearable sneakers, along with the fraction of the US adult population 20 years or older in each of five age groups. (1) Find the probability that the person owned at least five pairs of wearable sneakers. (2) Find the probability that the person selected was 65 years of age or older, given that the person owned at least five pairs of wearable sneakers. Groups and Ages G1 (20-24) G2 (25-34) G3 (35-49) G4 (50-64) G5 (≥65) Fraction with ≥ 5 pairs 0.26 0.2 0.13 0.18 0.14 Fraction of US Adult 20 and Older 0.09 0.18 0.3 0.25 0.18
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(a) What is the probability that a new customer has an accident over the first year of his contract? (b) A new customer has an accident during the first year of his contract. What is the probability that he belongs to the group likely to have an accident?