If you buy a lotterie ticket you have a chance to win, if you buy another one, the chance doubles, why is that?


If you buy a lotterie ticket that has a 1:100000 chances to win you have a 1:1000000 chance. If you buy two tickets, you have 2:1000000 or 1:500000 chance. Why can I eliminate 500.000 tickets with just one more ticket?

What am I conflating here?

Edit: Thank you guys, this was always something I started wondering about.

In: 0

You don’t “eliminate” anything.

1:100000 just means there’s 100000 possible outcomes (tickets to be drawn), and one of them (the one ticket you own) results in you winning. When you buy a 2nd one, there’s still 100000 possible tickets to be drawn, but two of them would result in you winning.

Saying you’re “eliminating” tickets is wrong. 1:500000 just means, if we were to select 500000 winning tickets then you’d have, on average, one winning ticket. It makes sense since you bought two tickets in a pool of a million.

I’m going to shrink the numbers so that I don’t have to count zeroes.

If a lottery has a 1:10 chance to win, then that means there are 10 tickets in total available.
If 11 people want to buy tickets, tough shit, one of them can’t.
There are only 10 possible numbers.
And you have one of them.

If you buy a second ticket, then you have 2 tickets, but there are still only 10 tickets in total, and you own 1/5 of them.
You haven’t “eliminated” 5 tickets.
Saying that your odds have improved to 1:5 means that if there *were* only 5 tickets and you had only 1 ticket, then your chances of winning would be the same as when you have 2 tickets out of a total of 10.

You don’t eliminate 500,000 tickets, you eliminate 1 way you *can’t* win.

So instead of having 999,999 ways you can’t win, you now only have 999,998 ways you can’t win. Which means you still double your chances of winning, but the chance you don’t win is still very ~~low~~ high.