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Raffle A service organization is selling $5 raffle tickets as part of a fundraising program. The first and second prizes are $3000 and $1000, respectively. In addition to the first and second prizes, there are 50 $20 gift certificates to be awarded. The number of tickets sold is 2000. Find the player’s expected net gain when one ticket is purchased.

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 18RE
Textbook Problem
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Raffle A service organization is selling $5 raffle tickets as part of a fundraising program. The first and second prizes are $3000 and $1000, respectively. In addition to the first and second prizes, there are 50 $20 gift certificates to be awarded. The number of tickets sold is 2000. Find the player’s expected net gain when one ticket is purchased.

To determine

To calculate: The player’s expected net gain on purchase of one $5 raffle ticket in which the first and the second prizes are $3000 and $1000 along with the 50 nos. of $20 gift certificates for a total number of tickets sold is 2000.

Explanation of Solution

Given Information:

A service organization sells $5 raffle ticket with the first and the second prizes as $3000 and $1000 along with the 50 nos. of $20 gift certificates and total number of tickets sold is 2000.

Formula used:

If a discrete random variable takes the values {x1,x2,,xm}, then the expected value of the random variable is defined as,

E(x)=x1P(x1)+x2P(x2)++xmP(xm)

Calculation:

Consider a service organization which sells $5 raffle ticket with the first and the second prizes as $3000 and $1000 along with the 50 nos. of $20 gift certificates and total number of tickets sold is 2000.

The four possible outcomes or the possible gains for the player with the probabilities are:

Case 1: If the player purchases $5 raffle ticket and gets the first prize $3000, then the possible gain is:

$3000$5=$2995

For a total of 2000 tickets sold, the probability of getting the first prize is:

P(1st prize)=12000

Case 2: If the player purchases $5 raffle ticket and gets the second prize $1000, then the possible gain is:

$1000$5=$995

For a total of 2000 tickets sold, the probability of getting the second prize is:

P(2nd prize)=12000

Case 3: If the player purchases $5 raffle ticket and gets the $20 gift certificates, then the possible gain is:

$20$5=$15

For a total of 2000 tickets sold, there are 50 Nos. of $20 gift certificates, so the probability of getting $20 gift certificate is:

P($20 gift certificate)=502000

Case 4: If the player purchases $5 raffle ticket and does not get any prize or gift certificate, then the player loses the amount paid for the ticket

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)
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Ch. 9.1 - In Exercises 3-6, evaluate the expression....Ch. 9.1 - In Exercises 3-6, evaluate the expression....Ch. 9.1 - In Exercises 7-10, write the fraction as a...Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - In Exercises 710, write the fraction as a percent....Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Sample Spaces and events In Exercises 14,...Ch. 9.1 - Finding Frequency and Probability Distributions In...Ch. 9.1 - Finding Frequency and Probability Distributions In...Ch. 9.1 - Random Selection In a class of 72 students, 44 are...Ch. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Determining a Missing Probability In Exercises 9...Ch. 9.1 - Determining a Missing Probability In Exercises 9...Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - 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