Jackpot set at $190,000,000 expected value

Question

Imagine you are doing research for a term paper in your English class and you have chosen the topic to be “The Benefits and Costs of My State's Lottery”. You find the following information for your state’s lottery:

Lottery summary
Prize Probability
Jackpot 1 in 160,000,000
$14,000 1 in 180,000
$600 1 in 14,000
$6 1 in 175
$2 1 in 60

You know that it costs $2 to purchase the lottery ticket in order to play the game. What would you conclude in your term paper regarding the expected value of the game (after purchasing the ticket), if the jackpot were to be set at $190,000,000?

Answer 1

Let's calculate the expected prize:

 

We omit P(Loss)(Loss prize) A loss prize is $0.

 

E(Prize) = 190,000,000/160,000,000 + 14,000/180,000 + 600/14,000 + 6/175 + 2/60

 

= 19/16 + 7/90 + 3/70 + 6/175 + 1/30

 

=  34669/25200 = 1.375...

 

This is less than $2 so this State Lottery has an edge over it's players. This is typical of lotteries.