Suppose that we have 4 coins such that if the ith coin is flipped, heads will appear with probability i/5, i = 1,2,...,4. When one of the coins is randomly selected and flipped, it shows tails. What is the conditional probability that it was the 3rd coin?

Suppose that we have 4 coins such that if the ith coin is flipped, heads will appear with probability i/5, i = 1,2,...,4. When one of the coins is randomly selected and flipped, it shows tails. What is the conditional probability that it was the 3rd coin?

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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Question

Suppose that we have 4 coins such that if the ith coin is flipped, heads will appear with probability i/5,
i = 1,2, ...,4. When one of the coins is randomly selected and flipped, it shows tails. What is the conditional
probability that it was the 3rd coin?

Expert Solution

Step 1: INTRODUCTION

In the realm of probability and chance, a perplexing scenario unfolds with four distinct coins, each bearing its own unique probability of showing heads when flipped. With probabilities ranging from 1/5 to 4/5, these coins offer a diverse range of outcomes. However, our inquiry pertains to a specific situation: when one of these coins is randomly chosen, flipped, and reveals tails, what is the conditional probability that it was, in fact, the elusive 3rd coin? In this question, we embark on a journey through conditional probability and Bayesian analysis to unravel the answer to this intriguing puzzle.

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