A charitable organization is running a raffle as a fundraiser. They offer a gran

Question

A charitable organization is running a raffle as a fundraiser. They offer a grand prize of $500, two second prizes or $100, and ten third prizes of $20 each. They will sell 1,000 raffle tickets. Let X represent the amount that will be won on an individual raffle ticket. 1. Write the probability mass function for X. 2. Calculate the average amount won on an individual raffle ticket. 3. Calculate the variance of X 4. If the organization wants to raise $1000 dollars of profit, for what price will they need to sell each raffle ticket?

Explanation / Answer

Lets draw the table, P(x) here is frequncy/total number of tickets

1. PMF is

P(X) = 0.001 when x = 500

= 0.002 when x = 100

= 0.01 when x =20

2. Avg amount won on an individual raffle ticket

= Mean = E(X) = sum(PiXi)

= 500*0.001 + 100*0.002 + 20*0.01

= 0.9

3. Variance = E(x2) - (E(x))2

= 5002*0.01 + 1002*0.02 + 202*0.01 - (0.9)2

= 274 - 0.81

= 273.19

4. Avg amount won on an individual raffle ticket = 0.9 (from 2)

for 1000 tickets avg amount won will be 0.90*1000 = $900

To make $1000 profit selling price total should be 1000+900 = $1900 for 1000 tickets

Thus, price on one ticket should be $1900/1000 = $1.90

x 500 100 20 Frequency 1 2 10 P(x) = Frequency/1000 0.001 0.002 0.01

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