Math Problem Statement

Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000 tickets are sold at $1.00 each and there is only one winner. What is the expected value per ticket for the organization? Question 10 options:

$0.17

-$0.81

-$0.17

$.83

Solution

To find the expected value per ticket for the organization, we need to consider both the revenue from selling the tickets and the cost of the prize.

  1. Revenue from tickets:
    The organization sells 3,000 tickets at $1 each, so the total revenue is: 3,000×1=$3,0003,000 \times 1 = \$3,000

  2. Cost of the prize:
    The prize is worth $500.

  3. Net revenue:
    The net revenue for the organization is the total revenue minus the cost of the prize: 3,000500=$2,5003,000 - 500 = \$2,500

  4. Expected value per ticket:
    Since the net revenue is $2,500 and 3,000 tickets are sold, the expected value per ticket for the organization is: 2,5003,000=2530=560.83\frac{2,500}{3,000} = \frac{25}{30} = \frac{5}{6} \approx 0.83

Therefore, the expected value per ticket for the organization is approximately $0.83.

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Math Problem Analysis

Mathematical Concepts

Probability
Expected Value
Revenue Calculation

Formulas

Total Revenue = Number of Tickets × Price per Ticket
Net Revenue = Total Revenue - Cost of Prize
Expected Value per Ticket = Net Revenue / Number of Tickets

Theorems

Basic principles of expected value

Suitable Grade Level

Grades 9-11