Decision tree diagram

Here is the photo I took on Wednesday. The quality isn't great, but you should be able to copy it to your clipboard and look at it in more detail. In fact, I just clicked on it (double click on a Mac, I don't know what you do with a PC) and Firefox presented it in a separate window, and the numbers were easily readable.



In addition to the decision tree we discussed the PowerBall lottery. p=1/80,000,000 to win, 200,000,000 tickets sold, $280,000,000 jackpot. The question is, does it pay (in an expected return sense) to enter? We immediately noticed that there might be more than one winner, and we estimated roughly 2.5 winners on average. This makes a ticket worth $1.41, so at first sight it appears to be a good idea to enter. But there are several problems, which we uncovered on further discussion. One is taxes: You would be taxed at the highest bracket, which is in the 35-39% range (depending on the tax law), as well as Vermont income tax. Also, you don't get the money all at once, but in installments over 20 years. To get the money at once, you have to take a discount of about 50% (since the way the lottery works, the state buys you an annuity that pays out over 20 years, and you would only get the amount that they would pay the insurance company to buy the annuity). Thus, it seems that it isn't worthwhile after all.

I left you with the problem of trying to get a more precise estimate of the expected return, considering the probability that 1, 2, 3,... more winners will win the lottery other than you.