Let’s take, for the sake of argument, a lottery system that draws 6 numbers out of a pool of 49. Order does not matter in systems of this size, except when there is a “power ball” type drawing and that ball is drawn from a separate pool of numbers. We’ll first calculate the odds of drawing a given set of numbers, and the compare that to some other, easier to understand probabilities.
The chance of getting a specific number on the first draw is fairly straight forward. In the lottery ball system, if we were to reach in and remove one ball from the container, we would have a 1 in 49 chance of drawing any single one of the balls. Simple. For the second ball, we have to change the dynamics a bit since the system has fundamentally changed. We already have one ball in our hand, so we’re not reaching into a container of 49 balls anymore, we’re drawing from 48 balls now. So our chance in of drawing a specific number in this phase is 1 in 48. Going to percentages, we went from a 1/49 (2.04%) chance to a 1/48 (2.08%) chance. In other words, our odds are increasing.
However, to match BOTH numbers in the drawing, we have to bring both probabilities together and find out what the chance is that we will hit our 1/49 and 1/48 draw at the same time. It turns out that if we multiply these numbers together, we find out our combined probability. In this case it’s 1 in 2352, or .0004%. Now, for reference, compare this to the probability that you’ll get your car stolen in Toledo, Ohio. One of the major insurance companies calculates this event as having a .0058% chance of happening. Putting the two ideas together, you have a great chance of having your car stolen in Toledo than you do of picking just two correct numbers out of a 49 number pool.
By now it should be fairly obvious where this is going. For 6 numbers out of a 49 number pool, we simply multiply every draw out to get a 1 in 10,068,347,520 chance of winning. Toss a 49 ball power number into the equation and it jumps to 1 in 493,349,028,480. This is roughly equivalent to the chance that you’ll get struck by lightning two and a half times in one day, or flip a penny 39 times in a row and get heads every time.
Allen is a math enthusiast who loves statistics and the lottery. He enjoys playing the Michigan Lottery and helping others with Michigan Lottery information.
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