KIn finance, one example of a derivative is a financial asset whose value is determined (derived) from a bundleof various assets, such as mortgages. Suppose a randomly selected mortgage in a certain bundle has aprobability of 0.07 of default.(a) What is the probability that a randomly selected mortgage will not default?(b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood anyone mortgage being paid off is independent of the others? Note: A derivative might be an investment that onlypays when all nine mortgages do not default.(c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of themortgages defaults.(a) The probability is 0.93(Type an integer or a decimal. Do not round.)(b) The probability is 0.5204(Round to four decimal places as needed.)(c) The probability is(Round to four decimal places as needed.).…

We have given that P(default) = 0.07

Answered: K In finance, one example of 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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A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 0.9, $50 0.1. Over many weeks, what is a worker 's expected weekly bonus?
(Devore: Section 2.4 #59) At a certain gas station, 40% of the customers use regular gas (A₁), 35% use plus gas (A₂), and 25% use premium A3. Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. (a) What is the probability that the next customer will request plus gas and fill the tank (A₂B)? (b) What is the probability that the next customer fills the tank? (c) If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?
Example 3. A preliminary test is customarily given to the students at the beginning of a certain course. The following data are accumulated after several years: (a) 95% of the students pass the course, 5% fail. (b) 96% of the students who pass the course also passed the preliminary test. (c) 25% of the students who fail the course passed the preliminary test. What is the probability that a student who has failed the preliminary test will pass the course? Fail 95% preliminary test pass course 5% fail Figure 3.4 Let A be the event "fails preliminary test" and B be the event “Passes course." The probability we want is then PA(B) in (3.8), so we need P(AB) and P(A). P(AB) is the probability that the student both fails the preliminary test and passes the course; this is P(AB) = (0.95)(0.04) = 0.038. (See Figure 3.4; 95% of the students passed the course and of these 4% had failed the preliminary test.) We also want P(A), the probability that a students fails the preliminary test; this event…
A barbershop is operated by one barber and has a space capacity to accommodate for a total of 6 customers (including the one in service). If a customer comes to this shop and finds it full, he goes to other shops. Customers arrive according to Poisson distribution at a rate of 4.1 customers per hour. The barber’s service time is exponential and he can serve at a rate of 7.1 customers per hour. a. What is the probability that the barber is free? Answer = Answer b. What is the expected number of people in the system? Answer = Answer c. What is the expected waiting time in the queue? Answer = Answerhours. (hint: use effective arrival rate)
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In the game of roulette, a player can place a $6 bet on the number 11 and have a ag probability of winning. If the metal ball lands on 11, the player gets to keep the $6 paid to play the game and the player is awarded an additional $210. Otherwise, the player is awarded nothing and the casino takes the player's $6. Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is $ (Round to the nearest cent as needed.)

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