Consider a gambler who starts with an initial fortune of $1 and then on each successive gam- ble either wins $1 or loses $1 independent of the past with probabilities 0.45 and 0.55 respectively. The gambler's objective is to reach a total fortune of $10, without first getting ruined (running out of money). If the gambler succeeds, then the gambler is said to win the game. In any case, the gambler stops playing after winning or getting ruined, whichever happens first. What is the probabilty that the gambler wins the game?

Consider a gambler who starts with an initial fortune of $1 and then on each successive gam- ble either wins $1 or loses $1 independent of the past with probabilities 0.45 and 0.55 respectively. The gambler's objective is to reach a total fortune of $10, without first getting ruined (running out of money). If the gambler succeeds, then the gambler is said to win the game. In any case, the gambler stops playing after winning or getting ruined, whichever happens first. What is the probabilty that the gambler wins the game?

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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