Question

English and American spellings are rigour and rigor, respectively. A man staying at a Parisian hotel writes this word, and a letter taken at random from his spelling is found to be a vowel. If 40 percent of the English-speaking men at the hotel are English and 60 percent are Americans, what is the probability that the writer is an Englishman?

Name: Problem 29, Chapter 3: A First Course in Probability
Uploaded: 2022-01-22T14:16:49-08:00
Duration: 3 min 11 s
Channel: Wendi Zhao
Description: English and American spellings are rigour and rigor, respectively. A man staying at a Parisian hotel writes this word, and a letter taken at random from his spelling is found to be a vowel. If 40 percent of the English-speaking men at the hotel are English and 60 percent are Americans, what is the probability that the writer is an Englishman?

   English and American spellings are rigour and rigor, respectively. A man staying at a Parisian hotel writes this word, and a letter taken at random from his spelling is found to be a vowel. If 40 percent of the English-speaking men at the hotel are English and 60 percent are Americans, what is the probability that the writer is an Englishman?

A First Course in Probability

Sheldon M. Ross 5th Edition

Chapter 3, Problem 29

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Solved by Expert Wendi Zhao

01/22/2022

Step 1

We know that the probability that a man is English is 40% or 0.4, and the probability that a man is American is 60% or 0.6. Show more…

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English and American spellings are rigour and rigor, respectively. A man staying at a Parisian hotel writes this word, and a letter taken at random from his spelling is found to be a vowel. If 40 percent of the English-speaking men at the hotel are English and 60 percent are Americans, what is the probability that the writer is an Englishman?

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Key Concepts

Law of Total Probability

The Law of Total Probability provides a way to break down complex probability calculations into simpler parts by considering all possible ways an event can occur. It involves summing the probabilities of the event over a partition of the sample space based on different conditions or scenarios.

Bayes' Theorem

Bayes' Theorem is a fundamental concept in probability theory that allows one to update the probability of a hypothesis based on new evidence. It relates the conditional probability of the hypothesis given the evidence to the likelihood of observing the evidence given the hypothesis and the prior probability of the hypothesis.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. It is essential in problems where the outcome depends on the occurrence of certain conditions or evidence.

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