/*! 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 30 In a sweepstakes sponsored by Ge... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 30

In a sweepstakes sponsored by Gemini Paper Products, 100,000 entries have been received. If 1 grand prize, 5 first prizes, 25 second prizes, and 500 third prizes are to be awarded, what is the probability that a person who has submitted one entry will win a. The grand prize? b. A prize?

Short Answer

Expert verified
a. The probability of winning the grand prize is \(0.00001\) or \(0.001\%\). b. The probability of winning a prize is \(0.00531\) or \(0.531\%\).

Step by step solution

01

Find the probability of winning the grand prize

To find the probability of winning the grand prize, we need to use the basic probability formula. There is only one grand prize to be won, so the number of successful outcomes is 1. The total number of outcomes is the total number of entries, which is 100,000. Probability of winning the grand prize: \(P(\text{grand prize}) = \frac{1}{100,000}\)
02

Find the probability of winning a prize

To find the probability of winning a prize, we need to calculate the total number of prizes to be won. There are 1 grand prize, 5 first prizes, 25 second prizes, and 500 third prizes. Number of all prizes: \( 1 + 5 + 25 + 500 = 531\) Now, we can use the basic probability formula again with the number of successful outcomes being the number of total prizes (531) and the total number of outcomes being the total number of entries (100,000). Probability of winning a prize: \(P(\text{prize}) = \frac{531}{100,000}\)
03

Simplify the probabilities (Optional)

By simplifying the fractions, we can provide the probabilities in reduced form. Probability of winning the grand prize: \(P(\text{grand prize}) = \frac{1}{100,000} = 0.00001\) Probability of winning a prize: \(P(\text{prize}) = \frac{531}{100,000} = 0.00531\) Thus, the final probabilities are given as: a. The probability of winning the grand prize is 0.00001 or 0.001%. b. The probability of winning a prize is 0.00531 or 0.531%.

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

Fifty people are selected at random. What is the probability that none of the people in this group have the same birthday?

According to a study of 100 drivers in metropolitan Washington D.C. whose cars were equipped with cameras with sensors, the distractions and the number of incidents (crashes, near crashes, and situations that require an evasive maneuver after the driver was distracted) caused by these distractions are as follows: $$ \begin{array}{lccccccccc} \hline \text { Distraction } & A & B & C & D & E & F & G & H & I \\ \hline \text { Driving Incidents } & 668 & 378 & 194 & 163 & 133 & 134 & 111 & 111 & 89 \\ \hline \end{array} $$ where \(A=\) Wireless device (cell phone, PDA) $$ \begin{aligned} B &=\text { Passenger } \\ C &=\text { Something inside } \mathrm{car} \\ D &=\text { Vehicle } \\ E &=\text { Personal hygiene } \\ F &=\text { Eating } \\ G &=\text { Something outside car } \\ H &=\text { Talking/singing } \\ I &=\text { Other } \end{aligned} $$ If an incident caused by a distraction is picked at random, what is the probability that it was caused by a. The use of a wireless device? b. Something other than personal hygiene or eating?

According to a study conducted in 2003 concerning the participation, by age, of \(401(\mathrm{k})\) investors, the following data were obtained: $$ \begin{array}{lccccc} \hline \text { Age } & 20 \mathrm{~s} & 30 \mathrm{~s} & 40 \mathrm{~s} & 50 \mathrm{~s} & 60 \mathrm{~s} \\ \hline \text { Percent } & 11 & 28 & 32 & 22 & 7 \\ \hline \end{array} $$ a. What is the probability that a \(401(\mathrm{k})\) investor selected at random is in his or her 20 s or 60 s? b. What is the probability that a \(401(\mathrm{k})\) investor selected at random is under the age of 50 ?

In "The Numbers Game," a state lottery, four numbers are drawn with replacement from an urn containing balls numbered \(0-9\), inclusive. Find the probability that a ticket holder has the indicated winning ticket. Three digits in exact order

Let \(E\) be any cvent in a sample space \(S .\) a. Are \(E\) and \(S\) independent? Explain your answer. b. Are \(E\) and \(\varnothing\) independent? Explain your answer.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure 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.