/*! 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 46 You work 5 evenings each week at... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 46

You work 5 evenings each week at a bookstore. Your supervisor assigns you 5 evenings at random from the 7 possibilities. What is the probability that your schedule does not include working on the weekend?

Short Answer

Expert verified
The probability that the 5 evening shifts will not include weekend is \(\frac{1}{21}\).

Step by step solution

01

Calculate Total Possible Ways

First, calculate the total number of ways to schedule 5 evening shifts from 7 days of a week. This is done using the combination formula \(C(n, r) = \frac{n!}{r!(n-r)!}\), where n is the total number of items and r is the number of items to choose. Plug in n = 7 (7 days in a week) and r = 5 (5 evening shifts), we get \(C(7, 5) = \frac{7!}{5!(7-5)!} = 21\). So, there can be 21 different possibilities to schedule 5 shifts in a week.
02

Calculate Desired Ways

Secondly, we calculate the number of ways to schedule 5 evening shifts from 5 weekdays (Monday to Friday). Here, n = 5 (number of weekdays) and r = 5 (5 evening shifts). So, plug in these values into the combination formula, we get \(C(5, 5) = \frac{5!}{5!(5-5)!} = 1\). Hence, there is only 1 way to schedule 5 evening shifts without including the weekends.
03

Calculate Probability

The probability is the ratio of the number of desired ways to the total number of possible ways. Therefore, the probability that the 5 evenings will not include the weekends is \(\frac{1}{21}\).

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

Write a general rule for finding \(P(A \)or \(B\) or \(C)\) for (a) disjoint and (b) overlapping events \(A, B,\) and \(C .\)

Describe a real-life event that has a probability of 0. Then describe a real- life event that has a probability of 1.

Your friend has two standard decks of 52 playing cards and asks you to randomly draw one card from each deck. What is the probability that you will draw two spades?

In Exercises \(3-6,\) make a table and draw a histogram showing the probability distribution for the random variable. \(w=1\) when a randomly chosen letter from the English alphabet is a vowel and \(w=2\) otherwise.

In Exercises \(7-10\) , determine whether the events are independent. (See Examples 1 and \(2 . )\) A vase contains four white roses and one red rose. You randomly select two roses to take home. Use a sample space to determine whether randomly selecting a white rose first and randomly selecting a white rose second are independent events.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

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.