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c) If the loaded coin has a probability of p > of giving A and 1 - p of giving B, where 2 should you set your threshold for your strategy to maximize your probability of winning in a game of N flips? d) Taking p = 0.75 as before, if you could specify in advance how many flips you wanted before guessing the coin, how many flips should you ask for if you wanted to as few flips as possible but at least a 90% chance of winning? (assume you use an optimal threshold)

c) If the loaded coin has a probability of p > of giving A and 1 - p of giving B, where 2 should you set your threshold for your strategy to maximize your probability of winning in a game of N flips? d) Taking p = 0.75 as before, if you could specify in advance how many flips you wanted before guessing the coin, how many flips should you ask for if you wanted to as few flips as possible but at least a 90% chance of winning? (assume you use an optimal threshold)

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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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 ofN 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.
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 ofN 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.
c) If the loaded coin has a probability of p > of giving A and 1 - p of giving B, where should you set your threshold for your strategy to maximize your probability of winning in a game of N flips? d) Taking p = 0.75 as before, if you could specify in advance how many flips you wanted before guessing the coin, how many flips should you ask for if you wanted to as few flips as possible but at least a 90% chance of winning? (assume you use an optimal threshold)
Transcribed Image Text:c) If the loaded coin has a probability of p > of giving A and 1 - p of giving B, where should you set your threshold for your strategy to maximize your probability of winning in a game of N flips? d) Taking p = 0.75 as before, if you could specify in advance how many flips you wanted before guessing the coin, how many flips should you ask for if you wanted to as few flips as possible but at least a 90% chance of winning? (assume you use an optimal threshold)
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