Question

Patrick’s luck had changed over night – but not his skill at mathematical reasoning. The day after graduating from college he used the $20 that his grandmother had given him as a graduation gift to buy a lottery ticket. He knew his chances of winning the lottery were extremely low and it probably was not a good way to spend this money. But he also remembered from the class he took in business analytics that bad decisions some-times result in good outcomes. So he said to himself, "What the heck? Maybe this bad decision will be the one with a good outcome." And with that thought, he bought his lottery ticket.The next day Patrick pulled the crumpled lottery ticket out of the back pocket of his bluejeans and tried to compare his numbers to the winning numbers printed in the paper. When his eyes finally came into focus on the numbers they also just about popped out of his head. He had a winning ticket! In the ensuing days he learned that his share of the jackpot would give him a lump sum payout of about $500,000 after taxes. He knew what he was going to do with part of the money, buy a new car, pay off his college loans, and send his grandmother on an all expenses paid trip to Hawaii. But he also knew that he couldn’t continue to hope for good outcomes to arise from more bad decisions. So he decided to take half of his winnings and invest it for his retirement. So what do you think? Who is right, Josh or Peyton? And more important, why?

Answer 1

I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.

Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.

We will now look at the sense in each piece of advice!

Explanation:

JOSH

By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.

PEYTON

By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?

Analyzing with the figures given,

$20 gets Patrick a lottery ticket.

$250,000 will get him 12,500 lottery tickets!

Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.

So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000

If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.