Question

A charity is conducting a raffle to raise money. Tickets cost $2 each and it is expected that the charity will sell 8,000 tickets. The winning raffle tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $500, 5 prizes of $100, and 30 prizes of $5.What is expected value and create a probability distribution for this?

Answer 1

Let X be the winning amount in raffle tickets.

Probability to get the prize of $500 = P(X = 500) = 1/8000

Probability to get the prize of $100 = P(X = 100) = 5/8000

Probability to get the prize of $5 = P(X = 5) = 30/8000

Probability of no prize = P(X = 0) = 1 - (1/8000 + 5/8000 + 30/8000) = 7964 / 8000

The probability distribution of X is,

X	P(X)
0	7964 / 8000
5	30/8000
100	5/8000
500	1/8000

Expected value = E(X) = 0 * (7964 / 8000) + 5 * (30/8000) + 100 * (5/8000) + 500 * (1/8000)

= 0.14

Expected gain of charity from each ticket = 2 - 0.14 = 1.86

Total Expected gain of charity = 1.86 * 8,000 = $14880