Answer to Question #306055 in Statistics and Probability for pretty

Question

A school club is organizing a fundraising campaign by selling raffle tickets. There are 1000 tickets being sold at Php50 each and the prizes at stake are, a laptop worth Php35,000, a mobile cellphone worth Php10,000, and a cash prize of Php5,000. You buy 1ticket. What is the expected value of your gain?

Answer 1

Suppose we buy a lottery ticket for Php 50, we have one chance of winning a laptop worth Php35,000.The potential loss is the cost of the ticket: Php 50, while the potential gain is Php 35,000 less the cost of the Php 50 ticket (Php35,000 – $50) = Php 34,950

or

We buy the lottery ticket for Php 50, we have one chance of winning a mobile cellphone worth Php10,000.The potential loss is the cost of the ticket: Php 50, while the potential gain is Php 10,000 less the cost of the Php 50 ticket (Php10,000 – $50) = Php 9,950

or

We buy the lottery ticket for Php 50, we have one chance of winning cash prize worth Php5,000.The potential loss is the cost of the ticket: Php 50, while the potential gain is Php 5,000 less the cost of the Php 50 ticket (Php5,000 – $50) = Php 4,950.

Given that the lottery sells 1,000 tickets, the odds of winning are 1 in 1,000, or 1/1000. Since the odds of winning are 1/1000, then your odds of losing are 999 out of 1,000, or 999/1000.

Therefore,

The expected value= ((-50*0.999+ 34950*0.001) + (-50*0.999 +9,950*0.001)+ (-50*0.999 +4,950*0.001))/3 = −33.33

Answer: The expected value of our loss = Php -33.33