Nichols Math Professor Dissects Probability of Winning Mega Millions Jackpot

Are you vying for a piece of the $1.6 billion Mega Millions pie — or, preferably, all of it? Well, Heard on The Hill, asked Nichols College Associate Professor of Mathematics Mark Naigles what he thinks the chances are of someone winning the largest jackpot in Mega Millions history. The numbers will be drawn at 11 p.m. Tuesday, Oct. 23.

Here’s what Professor Naigles, Nichols’ resident probability expert, had to say:

For starters, we need to select five different numbers between 1 and 70.

Then we pick a number between 1 and 25.

Consider the first number we pick, we have 70 choices.

For the second number, we only have 69 choices since the numbers need to be different

For the third number, there are 68 choices

Fourth number, 67 choices

Fifth number, 66 choices

For the sixth number we have 25 choices.

Thus the total number of possibilities is 70*69*68*67*66*25 = 36,309,042,000

However, the order of the first 5 cards is irrelevant, so we need to divide this by the number of ways we can arrange those five cards, i.e. 5 factorial = 120

Thus the number of ways to win the jackpot is 36,309,042,000 / 120 = 302,575,350.

Thus the probability of winning the jackpot is 1 out of 302,575,350.

To put this in perspective, the probability of being struck by lightning in your lifetime is 1 in 700,000, so you’d need to be struck by lightning 1.5 times in your life to equal this likelihood.

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