Thursday, July 14, 2005

Unlucky in Pepsi, Lucky in Love?

So Pepsi's got this little promotion where 1 in 3 caps is supposed to be a winner of an iTunes song. Now, I don't use iTunes, but no one likes to be a loser. So opening the cap on the Pepsi that I drink most afternoons is always highly anticipated. (Pepsi is an afternoon cola, Coke is more of an evening beverage.)

It's been two weeks - 10 caps by my count. And I've won a total of one time. What are the odds of that? Well, I'll tell you.
  • Assuming a huge number of caps, the odds of getting a winner are independent for each cap (what I got on the last one doesn't impact what I get on the next one).
  • According to Pepsi, my odds of winning are 1 in 3.
  • According to what I recall from my old statistics classes, my odds of losing 9 times in 10 is 10*(1/3)*(2/3)^9. That is, there are 10 different combinations where 1 in 10 wins (only the first cap wins, only the second cap wins, etc.) and in each combination there are nine losers (2/3) and one winner (1/3).
That comes to 8.7%. Yes, the odds of anyone being this unlucky are greater than 91%.

I have two trips to Vegas coming up in October. I will not be bringing any spending cash.

Side note: The "inspection" method of weeding out the loser caps doesn't work in a vending machine.

[Update August 10, 2005] Finally! My luck has changed! This week two bottles that I opened were winners of a free iTunes song! Of course, the contest ended over a month ago, but still, I feel somewhat vindicated. I'm not unlucky, my luck is just delayed until it is worthless.

Anyone want to buy three unused Pepsi iTunes winning bottle caps?

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