Question

In the lottery game Fantasy 5 you have to select 5 numbers from the numbers {1,2,3,.......,38,39}. The jackpot today is $76,000. Each ticket costs $1. In this lottery each number must be different and the order of the numbers does not matter.

a.) What is the probability of having a winning ticket?

b.) What is the expected value of this game?

c.) A fair game has an expected value of 0. How large does the jackpot have to be for Fantasy Five to be a fair game?

Answer 1

a)

probability of having a winning ticket =P(selecting a ticket which match 5 out of 5 numbers)

=⁵C₅/³⁹C₅ =1/575757

b)

expected value =(1/575757)*76000-1= $-0.87

c)let winning amount is x:

for this to be fair

expected value =(1/575757)*x-1= 0

x=$575757