but that it's a sequence of numbers complicates things
It's the same principle, just on a MUCH larger scale. That it is a sequence of numbers doesn't factor in. The sequence of number just skyrockets the odds. It's still an exact sequence of numbers you're trying to pick.
You're still both right, Toe. It's just a different way to look at it. It's a classic "glass half empty, glass half full".
I need the mathematical explanation for why that is so.
Powerball odds are 1 in 175,223,510.
So, with one ticket the odds are 175,223,510 divided by 1, which is of course 1 in 175,223,510
buy 2 tickets, it's 175,223,510 divided by 2, which is 1 in 87,611,755 (her odds doubled)
buy 3 tickets, it's 175,223,510 divided by 3, which is 1 in 58,407,836.66 (her odds tripled)
If she bought half the number (87,611,755) of ticket, it would be 175,223,510 divided by 87,611,755 which is 1 in 2.
You certainly have a hundred more chances to win, but that is not the same thing as being 100 times more *likely* to win. Is it?
Yes, mathematically speaking she is exactly 100 times more likely to win when buying 100 instead of 1.
Though, she is still very unlikely to win even with those 1 in 17,522,235.1 odds.
How are the odds fig'd?? RHL was close, but you have to factor in a bit more...
In Powerball you pick 5 white balls between 1 and 59.
you also must pick 1 red ball between 1 and 35.
It doesn't matter in which order the white balls are picked, so your odds of picking one of the white balls on your first number is 5 in 59.
Now there are only 58 balls left, the odds of hitting that is 4 in 58.
57 balls are left with 3 balls left. Odds of hitting one of the them is 3 in 57.
Then 2 in 56.
Then 1 in 55.
This is calculated by taking multiplying all the chances together (59 x 58 x 57 x 56 x 55) or 600,766,320, THEN dividing by the number of picks (5 x 4 x 3 x 2 x 1) or 120.
This leaves us at 5,006,386.
Now, the odds of hitting the red ball is 1 in 35. So, multiply 35 by the odds of getting the white balls.
35 x 5,006,386 = 175,223,510.