25. Neighborhood Insurance sells fire insurance policies to local homeowners. The premiumis $110, the probability of a fire is .001, and in the event of a fire, the insured damages(the payout on the policy) will be $100,000. (LO 6-6)a. Make a table of the two possible payouts on each policy with the probability ofeach.b. Suppose you own the entire firm, and the company issues only one policy. What arethe expected value and variance of your profit?c. Now suppose your company issues two policies. The risk of fire is independentacross the two policies. Make a table of the three possible payouts along with theirassociated probabilities.d. What are the expected value and variance of your profit?e. Compare your answers to (b) and (d). Did risk pooling increase or decrease the vari-ance of your profit?f. Continue to assume the company has issued two policies, but now assume you takeon a partner, so that you each own one-half of the firm. Make a table of your share ofprthe possible payouts the company may have to make on the two policies, along withtheir associated probabilities.g. What are the expected value and variance of your profit?h. Compare your answers to (b) and (g). What has happened to your risk? What aboutyour expected profit?i. Comparing the answers to (e) and (h), what do you conclude about risk sharing ver-sus risk pooling?

Answered: Image /qna-images/answer/830457c4-fce6-4984-86f5-d8b780fb6092.jpg

Answered: 5. Neighborhood Insurance sells fire…

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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Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, two green ones, three white ones, and one purple one. She grabs six of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She has at most one green one.
Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, three green ones, two white ones, and two purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She has at most one green one.
You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent
Tom has a standard set of pool balls. If he were to draw one ball at random, what is the probability that it will be red or yellow? Give your answer in its simplest form.
The table below shows the probability of winning 0-5 dollars playing a game. Amount Won ($) 0 1 2 3 4 5 Probability 4/24 7/24 7/24 3/24 2/24 1/24 The stallholder charges $2.50 for each playing of the game. How much money can the stallholder expect to make for the charity on a day when there are 400 plays of the game?
Alex, Natasha, and Juan fill orders in a fast-food restaurant. Alex incorrectly fills 20% of the orders he takes. Natasha incorrectly fills 12% of the orders she takes. Juan incorrectly fills 5% of the orders he takes. Alex fills 30% of all orders, Natasha fills 45% of all orders, and Juan fills 25% of all orders. An order has just been filled. A. If the order was filled by Juan, what is the probability that it was filled correctly? B. Who filled the order is unknown, but the order was filled incorrectly. What are the revised probabilities that Alex, Natasha, or Juan filled the order? C. Who filled the order is unknown, but the order was filled correctly. What are the revised probabilities that Alex, Natasha, or Juan filled the order?

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