Imagine you are doing research

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 180,000,000
$15,000 1 in 100,000
$600 1 in 10,000
$9 1 in 160
$3 1 in 80

You know that it costs $3 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 (including purchasing the ticket), if the jackpot were to be set at 190,000,000?

Answer 1

1) Figure out how often the ticket pays out, which is the sum probabilities listed above.

 

(1/180M) + 1/100k + 1/10k + 1/160 + 1/80 = .0188

 

2) Figure out how often the ticket DOES NOT pay out.

 

1 - P(ticket pays out)

1- .0188

.9812

 

3) Calculate the expected value of the ticket.

 

EV = Sum of P(each event) * Payout(each event)

=[(1/180M) * 190M]  + [(1/100,000)*15000] + [(1/10000) * 600] + [(1/160)*9] + [(1/80) * 3) + [.9812*-3]

=190/180 + 15/100 + 600/10000 + 9/160 + 3/80 + [.9812*-3]

=-$1.584

 

So you will lose ~$1.58 on the average ticket.