The last post about the probability of tossing a coin and getting 10 heads in a row prompted a question about the lottery. The conversation between Leonard's mother Beverly and Sheldon on the Big Bang Theory comes to mind:
Beverly: Is that a rhetorical point, or would you like to do the math?
Sheldon Cooper: I'd like to do the math.
Beverly: I'd like that, too.
Here we go. Say there are 44 possible numbers and you have to pick the lucky 6 to win. How many ways are there of choosing a 6-number combo from the 44?
The formula is C (44,6) which is 44 factorial divided by (6 factorial x 38 factorial) or 44! / (6! *38!). Then the probability of coming up with a specific 6 number combination is 1 over that number.
Refresher: Factorial is the product of that number and all the positive integers less than it. So, 6 factorial, designated as 6! is the product of 6x5x4x3x2x1 or 720. Factorial get huge fast. For example, 10! is 3,628,800. So 44! is huge and 1/44! is minute.
To see the chances for a particular lucky number being in the selected 6, you want to find the probability that the winning 6 number combination will contain any given number. First, you want to figure out how to not pick that number.
You have to choose the 6 numbers from the other 43 so use the formula C(43, 6). There are C(44,6) - C(43,6) combinations which include your lucky number.
The probability is then that result divided by C(44,6).
Moral? Don't quit your job to win the lottery.
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