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4. This questions is adopted from the Martingale doubling system question in Homework 1. In roulette, the probability of red is 18/38. Suppose you bet on red and use the Martingale doubling system: every time you win, bet $1 next time; every time you lose, double your previous bet. Suppose you play this game until you have won more than $20 or you have lost more than $50. Use simulation to answer the following questions. (1) What is the probability that you end up winning more than $20 at the end? (2) On average, how many games will you be playing? (3) Estimate the distribution of the game length by plotting a histogram.

4. This questions is adopted from the Martingale doubling system question in Homework 1. In roulette, the probability of red is 18/38. Suppose you bet on red and use the Martingale doubling system: every time you win, bet $1 next time; every time you lose, double your previous bet. Suppose you play this game until you have won more than $20 or you have lost more than $50. Use simulation to answer the following questions. (1) What is the probability that you end up winning more than $20 at the end? (2) On average, how many games will you be playing? (3) Estimate the distribution of the game length by plotting a histogram.

A First Course in Probability (10th Edition)
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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4. This questions is adopted from the Martingale doubling system question in Homework 1. In roulette, the probability of red is 18/38. Suppose you bet on red and use the Martingale doubling system: every time you win, bet $1 next time; every time you lose, double your previous bet. Suppose you play this game until you have won more than $20 or you have lost more than $50. Use simulation to answer the following questions. (1) What is the probability that you end up winning more than $20 at the end? (2) On average, how many games will you be playing? (3) Estimate the distribution of the game length by plotting a histogram.
Transcribed Image Text:4. This questions is adopted from the Martingale doubling system question in Homework 1. In roulette, the probability of red is 18/38. Suppose you bet on red and use the Martingale doubling system: every time you win, bet $1 next time; every time you lose, double your previous bet. Suppose you play this game until you have won more than $20 or you have lost more than $50. Use simulation to answer the following questions. (1) What is the probability that you end up winning more than $20 at the end? (2) On average, how many games will you be playing? (3) Estimate the distribution of the game length by plotting a histogram.
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