Instead of investing your retirement money in a 401(k) plan, you decide to “inve
ID: 3277117 • 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.
Should you be investing your money in Mega Millions tickets if you are trying to save for your retirement (vs just playing for entertainment)? (yes or no)
P(x) 1.00 1/258,890,850 1/18,492,204 1/739,688 1/52.835 1/10,720 1/766 1/473 1/56 1/21 Payoffx)Px)*Payoff(x) Ticket price 5 w+1 100,000,000 1,000.000 5,000 500 50 3 w+1 2w+1 1w+1 0w+1Explanation / Answer
As the expected payoff is negative, one should not be investing in Mega Millions tickets if the savings are for retirement.
P(x) Payoff(x) P(x)*Payoff(x) 1 -1 -1 1/258890850 100,000,000 0.386263168 1/18492204 1,000,000 0.054076842 1/739688 5,000 0.006759607 1/52835 500 0.009463424 1/10720 50 0.004664179 1/766 5 0.006527415 1/473 5 0.010570825 1/56 2 0.035714286 1/21 1 0.047619048 E = -0.438341207