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As you are in gym class, you find out that your classmates are playing a game. A player will show you two coins, one of which is fair (each outcome with equal probability), the other of which is "loaded", giving side A with probability of 0.75 and side B with probability of 0.25 The player will then select one of these coins at random and flip a number of times, at which point you have to guess based on the results what coin it is.

As you are in gym class, you find out that your classmates are playing a game. A player will show you two coins, one of which is fair (each outcome with equal probability), the other of which is "loaded", giving side A with probability of 0.75 and side B with probability of 0.25 The player will then select one of these coins at random and flip a number of times, at which point you have to guess based on the results what coin it is.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Answer the following questions accordingly. Thanks in advance!

As you are in gym class, you find out that your classmates are playing a game. A player will show you two coins, one of which is fair (each outcome with equal probability), the other of which is "loaded", giving side A with probability of 0.75 and side B with probability of 0.25. The player will then select one of these coins at random and flip a number of times, at which point you have to guess based on the results what coin it is. You decide on the following strategy: Out of N flips, if over half of them are A, you'll say it's the loaded coin, otherwise you'll say it's the fair coin. a) Following the strategy, what's the probability you win in a game of 10 flips? 20 flips? b) If you want to maximize your probability of winning, what threshold should you set for your strategy in a game of 10 flips? 20 flips? Try to be thorough to your methods (be precise)!
Transcribed Image Text:As you are in gym class, you find out that your classmates are playing a game. A player will show you two coins, one of which is fair (each outcome with equal probability), the other of which is "loaded", giving side A with probability of 0.75 and side B with probability of 0.25. The player will then select one of these coins at random and flip a number of times, at which point you have to guess based on the results what coin it is. You decide on the following strategy: Out of N flips, if over half of them are A, you'll say it's the loaded coin, otherwise you'll say it's the fair coin. a) Following the strategy, what's the probability you win in a game of 10 flips? 20 flips? b) If you want to maximize your probability of winning, what threshold should you set for your strategy in a game of 10 flips? 20 flips? Try to be thorough to your methods (be precise)!
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