(2) Here's a problem that pops up in actuarial science fairly often: it's called gambler's ruin.In each round of the game, you toss a fair coin. If it lands "Heads", you win $1; but ifit lands "Tails", you lose $1. If you don't have any money left after that, you must stopplaying. Suppose you start with $100. What is the probability you will get to $500 withoutfirst getting ruined (i.e. running out of money)?Let W be the event that you win, i.e. you reach 500 dollars without running out of moneyfirst. Let's break this up into steps:(a)(c)et P(Wn) be the conditional probability that you win if you start with ndollars. Use the Law of Total Probability (splitting up this probability into two cases:either you win the first flip, or you lose the first flip), and the fact that all flips areindependent to prove the following difference equation for P(Wn):P(W/n) = P(Wn+1)+P(W\n-1).arranging the difference equation, we getP(Wn+1) P(W|n) = P(W\n) - P(W|n - 1).Using this fact, give the formula for P(W\n) in terms of n, and write a proof.To answer our original question, what is P(W|100)?1

Answered: (2) Here's a problem that pops up in…

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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Bob, the proprietor of Midway Lumber, bases his projections for the annual revenues of the company on the performance of the housing market. He rates the performance of the market as very strong, strong, normal, weak, or very weak. For the next year, Bob estimates that the probabilities for these outcomes are 0.15, 0.23, 0.41, 0.07, and 0.14, respectively. He also thinks that the revenues corresponding to these outcomes are $25, $18.9, $16.3, $17, and $8 million, respectively. What is Bob's expected revenue for next year? (Round your answer to two decimal places.)$ million
Dystopia county has three bridges. In the next year, the Elder bridge has a 11% chance of collapse, the Younger bridge has a 3% chance of collapse, and the Ancient bridge has a 17% chance of collapse. What is the probability that exactly one of these bridges will collapse in the next year? (Round your final answer to four decimal places. Do not round intermediate calculations.)
A player tosses two fair coins. He wins $ 5 if 2 heads occur, $ 2 if 1 head occurs and 1 if no head occurs. (i) (ii) Find his expected gain. How much should he pay to play the game if it is to be fair?
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If you charge $3 to play a game of chance and the expected value is - $2, then what is the fair price?
If two events A and B are independent and you know that P(A) = 0.70, what is the value of P(A | B)?
A game has an expected value to you of $400. It costs $400 to play, but if you win you receive $100,000 (including your $400 bet), for a net gain of $99,600. What is the probability of winning?
You have invested in three different stocks: Engineering Aces, Upton Clothiers, and Thompson Musical Instruments. Because you have diversified your stocks so well, the way they change is independent. The probabilities of the stocks changing in value by more than 10% in a given week are listed below. P(E) = 19% P(U) = 11% P(T) = 7% What is the probability that all three will change by more than 10% in the same week?
Bob, the proprietor of Midway Lumber, bases his projections for the annual revenues of the company on the performance of the housing market. He rates the performance of the market as very strong, strong, normal, weak, or very weak. For the next year, Bob estimates that the probabilities for these outcomes are 0.15, 0.23, 0.41, 0.10, and 0.11, respectively. He also thinks that the revenues corresponding to these outcomes are $25, $18.5, $16.8, $14, and $13 million, respectively. What is Bob's expected revenue for next year? (Round your answer to two decimal places.)$ million
Your friend rolls an "unusual" six-sided die many times. She reports the probabilities of the possible outcomes are about as follows: Number Rolled: 1 2 3 4 5 6 Probability: 0.20 0.20 0.10 0.10 0.10 (a) Complete the table above by calculating the probability of rolling a 4. (b) Your friend creates the following game using this "unusual" die. You will pay her $2 if she rolls an even number and she will pay you $3 if she rolls an odd number.Use the table from part (a) to fill in the probability model below: Outcome: Roll an even number Roll and odd number Amount: Probability: (c) What is the expected value of this game for you? (d) Is this a fair game, meaning that each of you can expect to win the same amount in the long run? Explain.
Bob, the proprietor of Midway Lumber, bases his projections for the annual revenues of the company on the performance of the housing market. He rates the performance of the market as very strong, strong, normal, weak, or very weak. For the next year, Bob estimates that the probabilities for these outcomes are 0.19, 0.27, 0.37, 0.07, and 0.10, respectively. He also thinks that the revenues corresponding to these outcomes are $20, $18.4, $16.8, $16, and $11 million, respectively. What is Bob's expected revenue for next year? (Round your answer to two decimal places.)
part ii

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