/*! 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} Q4E A school contains students in gr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q4E (page 25)

A school contains students in grades 1,2,3,4,5, and6. Grades 2,3,4,5, and 6 all contain the same number of students, but there are twice this number in grade 1. If a student is selected at random from a list of all the students in the school, what is the probability that she will be in grade 3?

Short Answer

Expert verified

The probability that she will be in grade 3 is 0.142857

Step by step solution

01

Given information

A school contains in grades 1,2,3,4,5, and 6. Grades 2,3,4,5 or 6 all contain the same number of students, but there is twice this number in grade 1.

02

Finding the total number of students

Let the number of student in the each grades 2,3,4,5 or 6 is m and the number of student in grade 1 is 2m

The total number of students is 7m

The number of students in grade 3 is m

03

Calculating the probability

Here, we need to select 1 student from grade 3 and 1 student from total number of students.

The probability of a randomly selected student from a list of all the students is in grade 3 is

\(\begin{aligned}{}\Pr \left( {{\rm{Selected}}\,{\rm{student}}\,{\rm{in}}\,{\rm{grade}}\,3} \right) &= \frac{{{\bf{Number}}\,{\bf{of}}\,{\bf{Favourable}}\,{\bf{outcomes}}}}{{{\bf{Total}}\,{\bf{outcomes}}}}\\ &= \frac{{{}^m{C_1}}}{{{}^{7m}{C_1}}}\\ &= \frac{{\frac{{m!}}{{1! \times \left( {m - 1} \right)!}}}}{{\frac{{7m!}}{{1! \times \left( {7m - 1} \right)!}}}}\\ &= \frac{m}{{7m}}\\ &= \frac{1}{7}\\ &= 0.142857\end{aligned}\)

Thus, the probability of a randomly selected student in grade 3 is 0.142857

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

Let S be the sample space for some experiment. Show that the collection of subsets consisting solely of S and \(\phi \) satisfies the three conditions required in order to be called the collection of events. Explain why this collection would not be very interesting in most real problems.

Suppose that a number x is to be selected from the real line S, and let A, B, and C be the events represented by the following subsets of S, where the notation\(\left\{ {x: - - - - - } \right\}\)denotes the set containing every point x for which the property presented following the colon is satisfied:

\(\begin{aligned}{}{\bf{A = }}\left\{ {{\bf{x:1}} \le {\bf{x}} \le {\bf{5}}} \right\}\\{\bf{B = }}\left\{ {{\bf{x:3 < x}} \le {\bf{7}}} \right\}\\{\bf{C = }}\left\{ {{\bf{x:x}} \le {\bf{0}}} \right\}\end{aligned}\)

Describe each of the following events as a set of real numbers:

\(\begin{aligned}{l}{\bf{a}}{\bf{.}}\;{{\bf{A}}^{\bf{c}}}\\{\bf{b}}{\bf{.}}\;{\bf{A}} \cup {\bf{B}}\\{\bf{c}}{\bf{.}}\;{\bf{B}} \cap {{\bf{C}}^{\bf{c}}}\\{\bf{d}}{\bf{.}}\;{{\bf{A}}^{\bf{c}}} \cap {{\bf{B}}^{\bf{c}}} \cap {{\bf{C}}^{\bf{c}}}\\{\bf{e}}{\bf{.}}\;\left( {{\bf{A}} \cup {\bf{B}}} \right) \cap {\bf{C}}\end{aligned}\)

Suppose that X is a random variable for which \({\bf{E}}\left( {\bf{X}} \right){\bf{ = 10}}\) ,\({\bf{P}}\left( {{\bf{X}} \le {\bf{7}}} \right){\bf{ = 0}}{\bf{.2}}\,\,{\bf{and}}\,{\bf{P}}\left( {{\bf{X}} \ge {\bf{13}}} \right){\bf{ = 0}}{\bf{.3}}\) .Prove that,\({\bf{Var}}\left( {\bf{X}} \right) \ge \frac{{\bf{9}}}{{\bf{2}}}\) .

A box contains 24 light bulbs, of which four are defective. If a person selects four bulbs from the box at random, without replacement, what is the probability that all four bulbs will be defective?

Which of the following two numbers is larger:\(\left( \begin{aligned}{}93\\30\end{aligned} \right)\)or\(\left( \begin{aligned}{}93\\31\end{aligned} \right)\)?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied 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.