So, turns out I might have misheard SK when he said ChatGPT said 90%. That was for 1 ticket. For 2 tickets it is indeed 67%.

If we look at the 25 “tries”, each try has a 4500/50000 = 0.09 chance of winning. To get 2 tickets, we need to avoid the chances of getting no tickets or just one ticket.

To get no ticket, the prob is 0.91 ^ 25. (each not succeeding). = 0.0946 = 9.46%
This means the probability of getting at least one ticket is 1-0.0946 = 90.54%

Now, strictly speaking, it is a little more complicated. Once the the first time it did not work, the probability of the second time will work is actually 4500/49999 and then the next would be 4500/49998…. but the difference is going to be de minimis.

The probability of only one success means one succeeds but all else fails.

Which is 0.09 * (0.91 ^ 24) =

However, this itself can happen in 25 ways. So the total prob of only one success is 25 * 0.09 * (0.91 ^ 24) = 0.2340 = 23.40%

Thus the probability of getting two tickets is 100% – 9.46% – 23.40% = 67.14%