/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 450 A committee is composed of six D... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 450

A committee is composed of six Democrats and five Republicans. Three of the Democrats are men, and three of the Republicans are men. If a man is chosen for chairman, what is the probability that he is a Republican?

Short Answer

Expert verified
The probability that the chairman is a Republican given that he is a man is \(\frac{1}{2}\) or 50%.

Step by step solution

01

Calculating the total number of members

Find the total number of members in the committee. There are 6 Democrats and 5 Republicans, therefore a total of 11 members.
02

Calculate the number of men

Find the total number of men in the committee. There are 3 male Democrats and 3 male Republicans, therefore a total of 6 men.
03

Calculate P(B), the probability that the chairman is a man

To calculate P(B), divide the total number of men by the total number of committee members: P(B) = (Number of Men) / (Total Number of Members) P(B) = 6 / 11
04

Calculate the number of male Republicans

We are given that there are 3 male Republicans in the committee.
05

Calculate P(A鈭〣), the probability that the chairman is a male Republican

To calculate P(A鈭〣), divide the total number of male Republicans by the total number of committee members: P(A鈭〣) = (Number of Male Republicans) / (Total Number of Members) P(A鈭〣) = 3 / 11
06

Calculate P(A|B), the probability that the chairman is a Republican given he is a man

Using the conditional probability formula, P(A|B) = P(A鈭〣) / P(B): P(A|B) = (3 / 11) / (6 / 11) The 11's cancel out: P(A|B) = 3 / 6
07

Simplify the probability

Simplify the probability by canceling out the common factor: P(A|B) = 1 / 2 The probability that the chairman is a Republican given that he is a man is 1/2 or 50%.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

On an examination, a student answers a series of 5 multiple-choice questions each of which has 3 choices. This student, unfortunately, doesn't know how to answer any of the questions. He decides to answer each question by choosing an answer at random. Find the probability that he answers all 5 questions correctly.

A coin is tossed 3 times. Find the probability that all are heads, (a) if it is known that the first is heads, (b) if it is known that the first 2 are heads, (c) if it is known that 2 of them are heads.

Find the probability that Event \(\mathrm{A}\), drawing a spade on a single draw from a deck of cards, and Event \(\mathrm{B}\), rolling a total of 7 on a single roll of a pair of dice, will both occur.

A bowl contains eight chips. Three of the chips are red and the remaining five are blue. If two chips are drawn successively, at random and without replacement, what is the probability that the first chip drawn is red and the second drawn is blue?

From an ordinary deck of playing cards, cards are drawn successively at random and without replacement. Compute the probability that the third spade appears on the sixth draw.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.