Instead of investing your retirement money in a 401(k) plan, you decide to “inve

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

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