EP INTRODUCTION TO PROBABILITY+STAT.
EP INTRODUCTION TO PROBABILITY+STAT.
14th Edition
ISBN: 2810019974203
Author: Mendenhall
Publisher: CENGAGE L
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Chapter 4, Problem 4.135SE

a.

To determine

To find: the probability distribution for x ,the number of women chosen to be orchestra representatives.

a.

Expert Solution
Check Mark

Explanation of Solution

Given:

The board of directors of a major symphony orchestra has voted to create a committee for the purpose of handing employee complaints.

The committee consists of the president and the vice president of the symphony board and two orchestra representatives.

Calculation:

According to the question,

Let x be the number of women chosen to be orchestra representatives.

Let M1,M2,M3,M4 represents the four men and W1,W2 represents the two women candidates for choice of orchestra representatives.

Therefore, the simple events are

  M1M2,M1M3,M1M4,M1W1,M1W2M2M3,M2M4,M2W1,M2W2M3M4,M3W1,M3W2M4W1,M4W2W1W2

Let x represent x are chosen as representatives in the table.

    xAssociated simple events P(x)
    0M1M2,M1M3,M1M4,M2M3,M2M4,M3M4,615=25
    1M1W1,M1W2,M2W1,M2W2,M3W1,M3W2,M4W1,M4W2815
    2W1W2115

b.

To determine

To find: the probability that both the orchestra representatives will be women.

b.

Expert Solution
Check Mark

Answer to Problem 4.135SE

  P( women orchestra representatives  )=115

Explanation of Solution

Given:

The board of directors of a major symphony orchestra has voted to create a committee for the purpose of handing employee complaints.

The committee consists of the president and the vice president of the symphony board and two orchestra representatives.

Calculation:

According to the solution of part a,

The total number of events is 15 and the sample space for women orchestra representatives is W1W2

Therefore, the probability that both the orchestra representatives will be women is:

  P( women orchestra representatives  )=115 .

c.

To determine

To find: the mean and variance for the random variable x .

c.

Expert Solution
Check Mark

Answer to Problem 4.135SE

  μ=23;σ2=1645

Explanation of Solution

Given:

The board of directors of a major symphony orchestra has voted to create a committee for the purpose of handing employee complaints.

The committee consists of the president and the vice president of the symphony board and two orchestra representatives.

Calculation:

According to solution table in part a,

  P(only for  both the men)=25P(both men and women)=815P(only for  both the women)=115

Therefore, the mean and variance for the random variable x is:

  Mean, μ=xP(x)x=25(0)+815(1)+115(2)=815+215=1015=23

  Variance, σ2=xP(x)x2σ2=25(0)2+815(1)2+115(2)2( 2 3)2=815+41549=121549=1645

If A and B are independent, then P(A|B)=P(A) .

Hence, the mean and variance for the random variable x is μ=23;σ2=1645

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Chapter 4 Solutions

EP INTRODUCTION TO PROBABILITY+STAT.

Ch. 4.3 - Jury Duty Three people are randomly selected to...Ch. 4.3 - Prob. 4.12ECh. 4.3 - Tea Tasters A food company plans to conduct an...Ch. 4.3 - -Meter Run Four equally qualified runners, John,...Ch. 4.3 - Fruit Flies In a genetics experiment, the...Ch. 4.3 - Prob. 4.16ECh. 4.4 - You have two groups of distinctly different items,...Ch. 4.4 - Prob. 4.18ECh. 4.4 - Prob. 4.19ECh. 4.4 - Combinations Evaluate these combinations: a. C35...Ch. 4.4 - Choosing People In how many ways can youselect...Ch. 4.4 - Choosing People, again In how many ways canyou...Ch. 4.4 - Prob. 4.23ECh. 4.4 - Coins Four coins are tossed. How many simple...Ch. 4.4 - The Urn Problem, again Three balls are...Ch. 4.4 - What to Wear? You own 4 pairs of jeans, 12...Ch. 4.4 - Itineraries A businessman in New York is...Ch. 4.4 - Vacation Plans Your family vacation involves...Ch. 4.4 - A Card Game Three students are playing a cardgame....Ch. 4.4 - Dinner at Gerard’s A French restaurant offers...Ch. 4.4 - Playing Poker Five cards are selected from...Ch. 4.4 - Prob. 4.32ECh. 4.4 - A Hospital Survey A study is to be conducted in...Ch. 4.4 - Traffic Problems Two city council members are tobe...Ch. 4.4 - Prob. 4.35ECh. 4.4 - Prob. 4.36ECh. 4.4 - Prob. 4.37ECh. 4.4 - Cramming A student prepares for an exam bystudying...Ch. 4.4 - Monkey Business A monkey is given 12 blocks:3...Ch. 4.6 - An experiment can result in one of five equally...Ch. 4.6 - Refer to Exercise 4.40. Use the definition of a...Ch. 4.6 - Refer to Exercise 4.40. Use the definition of...Ch. 4.6 - Refer to Exercise 4.40. Use the Addition and...Ch. 4.6 - Prob. 4.44ECh. 4.6 - Suppose P(A)=.1 and P(B)=.5 . a. 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A college student frequents...Ch. 4.6 - Prob. 4.61ECh. 4.6 - Smoking and Cancer A survey of people in a...Ch. 4.6 - Smoke Detectors A smoke-detector system usestwo...Ch. 4.6 - Plant Genetics In 1865, Gregor Mendel suggesteda...Ch. 4.6 - Prob. 4.65ECh. 4.6 - Choosing a Mate Men and women often disagreeon how...Ch. 4.6 - Prob. 4.67ECh. 4.6 - Golfing Player A has entered a golf tournament but...Ch. 4.7 - Prob. 4.69ECh. 4.7 - Prob. 4.70ECh. 4.7 - Prob. 4.71ECh. 4.7 - Violent Crime City crime records show that 20%...Ch. 4.7 - Worker Error A worker-operated machine producesa...Ch. 4.7 - Airport Security Suppose that, in a particular...Ch. 4.7 - Football Strategies A particular football team is...Ch. 4.7 - No Pass, No Play Under the “no pass, no play”rule...Ch. 4.7 - Medical Diagnostics Different illnesses can...Ch. 4.7 - Cheating on Your Taxes? Suppose 5% of all...Ch. 4.7 - Screening Tests Suppose that a certain diseaseis...Ch. 4.8 - Discrete or Continuous? Identify the following as...Ch. 4.8 - Discrete or Continuous? II Identify the following...Ch. 4.8 - Probability Distribution I A random variable x has...Ch. 4.8 - Prob. 4.83ECh. 4.8 - Dice Let x equal the number observed on the throw...Ch. 4.8 - Grocery Visits Let x represent the number of times...Ch. 4.8 - If you toss a pair of dice, the sum T of the...Ch. 4.8 - RU Texting? The proportion of adults (18 years or...Ch. 4.8 - Which Key Fits? A key ring contains four office...Ch. 4.8 - Gender Bias? A company has five applicants for two...Ch. 4.8 - Defective Equipment A piece of electronic...Ch. 4.8 - Drilling Oil Wells Past experience has shown that,...Ch. 4.8 - Tennis, Anyone? Two tennis professionals, A and B,...Ch. 4.8 - Prob. 4.93ECh. 4.8 - Prob. 4.94ECh. 4.8 - Insuring Your Diamonds You can insure a $50,000...Ch. 4.8 - FDA Testing The maximum patent life for a new drug...Ch. 4.8 - Coffee Breaks Most coffee drinkers take a little...Ch. 4.8 - Prob. 4.98ECh. 4.8 - Actuaries A CEO is considering buying an insurance...Ch. 4 - Playing the Slots A slot machine has three slots;...Ch. 4 - Whistle Blowers Although there is legal...Ch. 4 - Prob. 4.102SECh. 4 - Refer to Exercise 4.102. By summing the...Ch. 4 - DVRs A retailer sells two styles of digital...Ch. 4 - Prob. 4.105SECh. 4 - Prob. 4.106SECh. 4 - Prob. 4.107SECh. 4 - Fire Alarms A fire-detection device uses three...Ch. 4 - Prob. 4.109SECh. 4 - Prob. 4.110SECh. 4 - Prob. 4.111SECh. 4 - Prob. 4.112SECh. 4 - Prob. 4.113SECh. 4 - Prob. 4.114SECh. 4 - Prob. 4.115SECh. 4 - Prob. 4.116SECh. 4 - Prob. 4.117SECh. 4 - Prob. 4.118SECh. 4 - Prob. 4.119SECh. 4 - Prob. 4.120SECh. 4 - Prob. 4.121SECh. 4 - Contract Negotiations Experience has shown...Ch. 4 - Prob. 4.123SECh. 4 - Prob. 4.124SECh. 4 - Prob. 4.125SECh. 4 - Prob. 4.126SECh. 4 - Mass Transit Only 40% of all people in a...Ch. 4 - Prob. 4.128SECh. 4 - Prob. 4.129SECh. 4 - Prob. 4.130SECh. 4 - Flextime A survey to determine the availability of...Ch. 4 - Prob. 4.132SECh. 4 - Pepsi™ or Coke™? 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