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 6number 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.
Top of Page
