MegaMillions Overlay?

[JinX11]

Ok, I gaffed on my last post - this situation isn't really comparable to the "Birthday Problem", which seeks to determine out of a certain population of people, what is the chance that any two members share the same birthday. This scenario is different - we don't want to know what is the chance that two people share the same numbers - we want to know what is the chance that one other person shares our (winning) number. It's still a factor of the population size, but unlike the "Birthday Problem", it doesn't scale as rapidly as the population size grows.

I have no idea how many entries are sold in the megamillions, so ultimately, I have no idea what the chance is someone will share your set of numbers. But, since there are P = 175711536 combinations (according to the odds posted), if the number of entries sold is given by n, I believe the probability formula would be given by:

1 - ((P-1)/P)^n.

So, at 100,000 entries, there is less than a 0.06% chance of someone sharing your winning numbers. At 1,000,000 entries, 0.57%; at 10,000,000 entries, it goes to 5.53%. I have no idea how many entries are typically sold in each drawing.