/*! 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 8 In a small city, approximately \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 8

In a small city, approximately \(15 \%\) of those eligible are called for jury duty in any one calendar year. People are selected for jury duty at random from those eligible, and the same individual cannot be called more than once in the same year. What is the probability that an eligible person in this city is selected 2 years in a row? 3 years in a row?

Short Answer

Expert verified
The probability that an eligible person in this city is selected 2 years in a row is \( 2.25 \% \), while for three years in a row it is \( 0.3375 \% \).

Step by step solution

01

Understand Independent Events

The selection of an eligible individual is made independently each year. The selection in any given year does not influence the selection in subsequent years. Hence, these are independent events.
02

Calculate the Probability for two consecutive years

Given that the probability of an eligible person being selected in a year is \( 15 \% \) or \( 0.15 \), the probability of an individual being selected two years in a row, due to the independence of the events, is given by the product of individual probabilities. So, it is \( 0.15 \times 0.15 = 0.0225 \) or \( 2.25 \% \).
03

Calculate the Probability for three consecutive years

Similar to step 2, the probability of being selected three years in a row is \( 0.15 \times 0.15 \times 0.15 = 0.003375 \) or \( 0.3375 \% \) .

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

The Associated Press (San Luis Obispo TelegramTribune, August 23,1995 ) reported on the results of mass screening of schoolchildren for tuberculosis (TB). It was reported that for Santa Clara County, California, the proportion of all tested kindergartners who were found to have TB was \(.0006\). The corresponding proportion for recent immigrants (thought to be a high-risk group) was \(.0075 .\) Suppose that a Santa Clara County kindergartner is to be selected at random. Are the outcomes selected student is a recent immigrant and selected student has \(T B\) independent or dependent outcomes? Justify your answer using the given information.

A radio station that plays classical music has a "by request" program each Saturday evening. The percentages of requests for composers on a particular night are as follows: \(\begin{array}{lr}\text { Bach } & 5 \% \\ \text { Mozart } & 21 \% \\ \text { Beethoven } & 26 \% \\ \text { Schubert } & 12 \% \\ \text { Brahms } & 9 \% \\ \text { Schumann } & 7 \% \\ \text { Dvorak } & 2 \% \\ \text { Tchaikovsky } & 14 \% \\ \text { Mendelssohn } & 3 \% \\ \text { Wagner } & 1 \%\end{array}\) Suppose that one of these requests is randomly selected. a. What is the probability that the request is for one of the three B's? b. What is the probability that the request is not for one of the two S's? c. Neither Bach nor Wagner wrote any symphonies. What is the probability that the request is for a composer who wrote at least one symphony?

Consider a system consisting of four components, as pictured in the following diagram: Components 1 and 2 form a series subsystem, as do Components 3 and 4 . The two subsystems are connected in parallel. Suppose that \(P(1\) works \()=.9\), \(P(2\) works \()=.9, P(3\) works \()=.9\), and \(P(4\) works \()=.9\) and that these four outcomes are independent (the four components work independently of one another). a. The \(1-2\) subsystem works only if both components work. What is the probability of this happening? b. What is the probability that the \(1-2\) subsystem doesn't work? that the \(3-4\) subsystem doesn't work? c. The system won't work if the \(1-2\) subsystem doesn't work and if the \(3-4\) subsystem also doesn't work. What is the probability that the system won't work? that it will work? d. How would the probability of the system working change if a \(5-6\) subsystem was added in parallel with the other two subsystems? e. How would the probability that the system works change if there were three components in series in each of the two subsystems?

Three friends \((\mathrm{A}, \mathrm{B}\), and \(\mathrm{C})\) will participate in a round-robin tournament in which each one plays both of the others. Suppose that \(P(\mathrm{~A}\) beats \(\mathrm{B})=.7, P(\mathrm{~A}\) beats \(\mathrm{C})\) \(=.8\), and \(P(\) B beats \(C\) ) \(=.6\) and that the outcomes of the three matches are independent of one another. a. What is the probability that \(\mathrm{A}\) wins both her matches and that B beats \(C\) ? b. What is the probability that A wins both her matches? c. What is the probability that A loses both her matches? d. What is the probability that each person wins one match? (Hint: There are two different ways for this to happen. Calculate the probability of each separately, and then add. )

The Los Angeles Times (June 14,1995 ) reported that the U.S. Postal Service is getting speedier, with higher overnight on-time delivery rates than in the past. Postal Service standards call for overnight delivery within a zone of about \(60 \mathrm{mi}\) for any first-class letter deposited by the last collection time posted on a mailbox. Two-day delivery is promised within a 600 -mi zone, and three-day delivery is promised for distances over \(600 \mathrm{mi}\). The Price Waterhouse accounting firm conducted an independent audit by "seeding" the mail with letters and recording on-time delivery rates for these letters. Suppose that the results of the Price Waterhouse study were as follows (these numbers are fictitious, but they are compatible with summary values given in the article): $$\begin{array}{lcc} & \begin{array}{c} \text { Number } \\ \text { of Letters } \\ \text { Mailed } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Letters Arriving } \\ \text { on Time } \end{array} \\ \hline \text { Los Angeles } & 500 & 425 \\ \text { New York } & 500 & 415 \\ \text { Washington, D.C. } & 500 & 405 \\ \text { Nationwide } & 6000 & 5220 \end{array}$$ Use the given information to estimate the following probabilities: a. The probability of an on-time delivery in Los Angeles b. The probability of late delivery in Washington, D.C. c. The probability that both of two letters mailed in New York are delivered on time d. The probability of on-time delivery nationwide
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.