   # 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. ### Calculus: An Applied Approach (Min...

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

#### Solutions

Chapter
Section ### 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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