How Lucky Can One Get?

A Texas woman just won $10 million and it turns out this wasn’t her first time!

Wow!!!  What are the chances of that happening?  The answer depends on a lot of variables: 1) the odds of winning each game; 2) the amount spent on tickets; and 3) the point in time of the odds calculation.

1) The Odds of Winning Each Game
The odds of winning her latest prize, the $140,000,000 Extreme Payout game, are 1:1,200,000.  If we were to calculate the odds of winning all four prizes and we assume that Ms. Ginther only bought one of each ticket (more on that later) we would multiple the odds of each game.  So, if the odds of the other game are 1:500,000, 1:2,000,000, and 1:250,000, then her odds of winning all four prizes would be 1:300,000,000,000,000,000,000,000!!!

2) Amount Spent on Tickets
The last calculation we made assumed that Ms. Ginther only bought one of each ticket.  But what if she bought more than one?  Let’s see how that variable will affect the odds of winning her latest prize, the $140,000,000 Extreme Payout game.  The odds of winning $10 million are 1:1,200,000.  Let’s assume that over the past year, Ms. Ginther (presumably still a wealthy woman from her past winnings) has purchased 100 of these $50 tickets for a total cost of $5,000.  Her odds of winning would now be much, much better: 1:12,000 (1,200,000 / 100 = 12,000).  So, let’s now assume the lucky winner bought 100 tickets of each game in which she won.  Her odds of winning would now be 1:3,000,000,000,000,000, which is still a very small chance!

3) The Point in Time of the Odds Calculation
This is another way of saying, what are the odds of Ms. Ginther winning one game?  Let’s go back in time to a few weeks ago before her latest win, and ask the following question: given that Ms. Ginther has already won 3 games, what are the odds of her winning $10 million playing the $140,000,000 Extreme Payout game if she buys 100 tickets?  Because all 4 events are independent of each other (one does not affect any other), her odds of winning would be just the odds of winning $10 million: 1:12,000.

So, the probability of Ms. Ginther winning all 4 games is indeed very, very small, but if we assume that she bought a large number of $50 tickets, her odds of winning just the $10 million are much, much better.