Question

A university organization annually holds a raffle event for fundraising purposes. The prizes include one $1000, three $500, and five $100. They would sell a total of one thousand tickets, in which a single ticket costs $5.

(a) Create a probability distribution table which includes the wins and losses.

(b) Find the expectation if a person buys one ticket. How much will this person win or lose?

(c) Is this raffle/game fair? Why or why not?

Answer 1

Given data:

Cost of the ticket is $5

Total number of ticket is 1000

prize table.

Prize	Number of prizes
$1000	1
$500	3
$100	5

a) probability for win = number of prizes /Total number of ticket

probability for loss = 1- proabability for win

Prize Xi	Number of prizes	Probability for win Pi	Probability for loss
$1000	1	0.001	0.999
$500	3	0.003	0.997
$100	5	0.005	0.995

b)

Expectation if anyone buy one ticket:

E(X) = sum of ( Xi*Pi)-cost of the ticket

E(X) =((1000*0.001)+(500*0.003)+(100*0.005))-5

E(X) =(1+1.5+0.5)-5=-2

Expectation if anyone buy one ticke is loss of $2

c)

in my point of view, this is not fair,

because we can see every expectation of every one is loss around $2 it means if anyone buy ticket prize of $5 he loss min 40% ($2), normal raffle game expectation should be min zero (mean no loss or no win)