Instead of investing your retirement money in a 401(k) plan, you decide to “inve
ID: 3303576 • Letter: I
Question
Instead of investing your retirement money in a 401(k) plan, you decide to “invest” the funds instead in Mega Millions lottery tickets. What is the average payoff (E) for each $1 ticket when the jackpot lump sum payoff is $100 million. Note: Since you do not get back the price of your $1 ticket even if you win, you are always guaranteed to lose $1. w = the number of correct white balls that you pick and y is if you pick the correct yellow mega ball.
x
P(x)
Payoff(x)
P(x)*Payoff(x)
Ticket price
1.00
-1
5 w + 1 y
1/258,890,850= 0.930991
100,000,000
5 w + 0 y
1/18,492,204= 0.00000005
1,000,000
4 w + 1 y
1/739,688=0.00000135
5,000
4 w + 0 y
1/52,835= 0.00001893
500
3 w + 1 y
1/10,720= 0.00009328
50
3 w + 0 y
1/766=0.00130548
5
2 w + 1 y
1/473=0.00211416
5
1 w + 1 y
1/560.01785714
2
0 w + 1 y
1/21=0.04761905
1
E =
x
P(x)
Payoff(x)
P(x)*Payoff(x)
Ticket price
1.00
-1
5 w + 1 y
1/258,890,850= 0.930991
100,000,000
5 w + 0 y
1/18,492,204= 0.00000005
1,000,000
4 w + 1 y
1/739,688=0.00000135
5,000
4 w + 0 y
1/52,835= 0.00001893
500
3 w + 1 y
1/10,720= 0.00009328
50
3 w + 0 y
1/766=0.00130548
5
2 w + 1 y
1/473=0.00211416
5
1 w + 1 y
1/560.01785714
2
0 w + 1 y
1/21=0.04761905
1
E =
Explanation / Answer
expected payoff = -0.43834
x P(x) Payoff(x) P(x)*Payoff(x) Ticket price 1 -1 -1 5 w + 1 y 3.86263E-09 10,00,00,000 0.386263168 5 w + 0 y 5.40768E-08 10,00,000 0.054076842 4 w + 1 y 1.35192E-06 5,000 0.006759607 4 w + 0 y 1.89268E-05 500 0.009463424 3 w + 1 y 0.00009328 50 0.004664 3 w + 0 y 0.00130548 5 0.0065274 2 w + 1 y 0.00211416 5 0.0105708 1 w + 1 y 0.017857143 2 0.035714286 0 w + 1 y 0.04761905 1 0.04761905 E -0.43834142