C. An insurance company calculates car insurance company calculates carinsurance premiums based on the age of the policyholder according to three agegroups: Group A consists of drivers younger than 22 years old; Group B consistsof drivers 22-33 years old, and Group C consists of drivers older than 33 years.Its portfolio consists of 10% Group A policyholders, 38% Group B policyholdersand 52% Group C policyholders.The probability of a claim in any 12 month period for a policy belonging to GroupA, B or C is 13%, 3% and 2%, respectively.(i) Calculate the probability that a randomly chosen policy holder from thisportfolio will make a claim during a 12 month period.One of the company's policyholders has just made a claim(ii) Calculate the probability that the policy holder is younger than 22 years.

Let us define some events A : a policy holder is from group A. B : a policy holder is from group B.…

Answered: (i) Calculate the probability that a…

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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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Phone calls arrive at the rate of 36 per hour at the reservation desk for Regional Airways. (a) Compute the probability of receiving six calls in a 5-minute interval of time. (b) Compute the probability of receiving exactly 10 calls in 20 minutes. (c) Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting? (d) If no calls are currently being processed, what is the probability that the agent can take 6 minutes for personal time without being interrupted by a call?
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High school seniors with strong academic records apply to the nation's most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admissions class, an Ivy League college received 2851 applications for early admission. Of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. Answer questions 3-5.
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An insurance agent sells the policies to 20 persons having same age and in good health. Based on the company's record, the probability that person in this age will live for the next 20 years is 2/3. Find the probability (a) 8 persons, (b) at most 7 persons, (c) more than 7 persons, (d) at least 3 persons, (e) more than 6 persons but less than 11 persons are still alive at the end of this 20 years period. The probability for a mango tree from a certain type, will produce fruits in the first year is 0.8. Each time, the mango trees seller sells about 5 trees to the buyer with the guarantee that if less than 3 trees produce fruits in the first year, he will replace them according to the number of trees which do not produce fruits. (a) Calculate the probability that there will no replacement. (b) If he sells the trees to 3000 buyers that are 5 trees to each buyer, how many trees are expected to be replaced?
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In a certain year, the probability that a stock was in the Information Technology sector was 0.1353. The probability that the stock had a dividend yield of 2.00% or higher given that it was in the Information Technology sector was 0.2988. The probability that a stock had a dividend yield of 2.00% or higher given that it was not in the Information Technology sector was 0.4469. Find the probability that the stock was in the Information Technology sector given that it had a dividend yield of 2.00% or higher. Let F be the event that a stock was in the Information Technology sector and E be the event that a stock had a dividend yield of 2.00% or higher. P(F)= and P P (F') =
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(i) Calculate the probability that a randomly chosen policy holder from this portfolio will make a claim during a 12 month period. One of the company's policyholders has just made a claim (ii) Calculate the probability that the policy holder is younger than 22 years.