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Someone has always got to win the lottery.

It is a very true statement that someone does win the lottery. However, the odds of me winning the lottery are extremely small. Another way to think about it is that it is highly unlikely that I will win the lottery, but it is less unlikely that I and two million other people won’t win the lottery.

In an earlier post, I discussed the probability of no one sharing the same birthday in a class of 28 students. There is only around a 35% chance that no two people will have the same birthday. The same logic can be applied to the lottery.

If the overall odds of winning the one million dollar Florida lottery is 1 in 125,000, then the probability of me winning (buying only one ticket) is .000008. It is sometimes helpful to imagine it in another way. The probability of me not winning is .999992 (1-.000008) or there is a 99.99% chance of me not winning the lottery.

However, someone has to win. When we think about the probability of me and one other person both not winning we still have a 99.99% chance of the two of us not winning (my odds of not winning, .999992 multiplied by her odds of not winning, .999992). Still not such a good gamble if we both played. However, if one hundred thousand people buy tickets, there is only a 45% chance that no one will win (.999992 multiplied by itself 100000 times). Thus, when so many people play, the chance that not one of them will win becomes very small. With the millions of tickets sold there is an extremely high probability that someone has to win.

I think I will save my dollar and let someone else win.