/*! 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 86 In a statistics class of 42 stud... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 86

In a statistics class of 42 students, 28 have volunteered for community service in the past. If two students are selected at random from this class, what is the probability that both of them have volunteered for community service in the past? Draw a tree diagram for this problem.

Short Answer

Expert verified
The probability that both randomly picked students are among the volunteers is \( \frac{C(28, 2)}{C(42, 2)} = 0.45 \). So, there is roughly 45% chance that two randomly picked students have both volunteered for community service. The tree diagram offers a visual representation of this setup.

Step by step solution

01

Calculate the total number of ways to select two students

We are given a class of 42 students and we are asked to calculate the probability of selecting two specific students. The number of ways this can be done is given by the combination formula \( C(n, r) = \frac{n!} {r!(n-r)!} \) where 'n' is the total number of items, 'r' is the number of items to choose, and '!' denotes the factorial of a number. In this problem, 'n' would be 42 (the total number of students) and 'r' would be 2 (the number of students being selected). We obtain \( C(42, 2) = \frac{42!}{2!(42-2)!} \)
02

Calculate the desired number of outcomes

We want both students to be among those who have volunteered. We are told that there are 28 students who have volunteered. So we want to calculate the number of ways to choose 2 students from these 28 volunteers. This is again calculated using the combination formula. This time 'n' would be 28 and 'r' would be 2. We obtain \( C(28, 2) = \frac{28!}{2!(28-2)!} \)
03

Calculate the probability

The probability is equal to the desirable outcomes divided by the total outcomes. We divide the result from step 2 by the result from step 1. This will give us the probability.
04

Draw a tree diagram

Start with one node symbolizing the total number of students. Draw two branches, one representing the volunteers and the other the students who haven't volunteered. From both of these nodes, draw two more nodes each, again representing volunteers and non-volunteers respectively. This gives you a visual representation of all possible scenarios when picking two students randomly.

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

A company that plans to hire one new employee has prepared a final list of six candidates, all of whom are equally qualified. Four of these six candidates are women. If the company decides to select at random one person out of these six candidates, what is the probability that this person will be a woman? What is the probability that this person will be a man? Do these two probabilities add up to \(1.0 ?\) If yes, why?

Powerball is a game of chance that has generated intense interest because of its large jackpots. To play this game, a player selects five different numbers from 1 through 59 , and then picks a Powerball number from 1 through 39 . The lottery organization randomly draws 5 different white balls from 59 balls numbered 1 through 59 , and then randomly picks a Powerball number from 1 through \(39 .\) Note that it is possible for the Powerball number to be the same as one of the first five numbers. a. If the player's first five numbers match the numbers on the five white balls drawn by the lottery organization and the player's Powerball number matches the Powerball number drawn by the lottery organization, the player wins the jackpot. Find the probability that a player who buys one ticket will win the jackpot. (Note that the order in which the five white balls are drawn is unimportant.) b. If the player's first five numbers match the numbers on the five white balls drawn by the lottery organization, the player wins about \(\$ 200,000\). Find the probability that a player who buys one ticket will win this prize.

Given that \(A\) and \(B\) are two independent events, find their joint probability for the following. a. \(P(A)=.61\) and \(P(B)=.27\) b. \(P(A)=.39\) and \(P(B)=.63\)

Let \(A\) be the event that a number less than 3 is obtained if we roll a die once. What is the probability of \(A ?\) What is the complementary event of \(A\), and what is its probability?

A certain state's auto license plates have three letters of the alphabet followed by a three-digit number. a. How many different license plates are possible if all three-letter sequences are permitted and any number from 000 to 999 is allowed? b. Arnold witnessed a hit-and-run accident. He knows that the first letter on the license plate of the offender's car was a \(\mathrm{B}\), that the second letter was an \(\mathrm{O}\) or a \(\mathrm{Q}\), and that the last number was a 5. How many of this state's license plates fit this description?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.