Mega-Millions Probability

You have heard what your chances of winning $ 640 million tonight are, so if you are curious how this is calculated here you go

“The numbers picked for the prizes consist of 5 numbers picked at random from a pool of 56 numbers (the White Numbers). Then a single number (the Mega Number) is picked from a second pool that has 46 numbers. If the results of these random number selections match one of the winning combinations on your lottery ticket, then you win something.

In any combinatorics problem where all possible outcomes are equally likely, the probability of a successful outcome is determined by finding the number of successful combinations, and then dividing by the total number of all combinations. There are nine possible configurations that will win something in the Mega Millions Lottery. For each of these, the probability of winning equals the number of winning combinations for that particular configuration divided by the total number of ways the Mega Millions numbers can be picked.
Mega Millions Total Combinations

Since the total number of combinations for Mega Millions numbers is used in all the calculations, we will calculate it first. The number of ways 5 numbers can be randomly selected from a field of 56 is: COMBIN(56,5) = 3,819,816. (See themath notation page or Help in Microsoft's Excel for more information on “COMBIN”).

For each of these 3,819,816 combinations there are COMBIN(46,1) = 46 different ways to pick the sixth number (the “Mega” number). The total number of ways to pick the 6 numbers is the product of these. Thus, the total number of equally likely Mega Millions combinations is 3,819,816 x 46 = 175,711,536.”

Credit Durango Bill

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Comments

[Kurt Marko]

Therefore, the expected value of a $1 lottery ticket is quite positive...looks like a great investment. :)

[vinnie mirchandani]

yes, but not as lucrative if multiple tickets have same number - as actually happened. And if they were pool tickets imagine all the legal and tax issues :)