You know, DB, I've been giving some more thought to the question of Buffy and I meeting in Vegas, and came up with yet another answer....
My first day there can be the first, second, or third day of one of her three visits, so there are 9 chances that she will be there the first day that I am.
But my second day there can only be the first day of one of her three visits. If it was the second or third day of one of her three visits, then we would have met on the first day.
Likewise, the third day of my visit.
So we have 15 opportunities to meet out of 365 days.
15/365, odds of about 23-1.
Which, I have a feeling, is also wrong.
Let's try it this way:
Yesterday, when you pointed out that a 1/40 chance occuring 40 times makes it a certainty, which is obviously impossible, you were correct.
If you flip a coin, you have a 50% chance of getting heads or tails. But on two flips, you can't add the 50% chances together and say there's a 100% chance of getting heads. You have to look at all the possible options
HH HT TH TT
So there is a 75% chance of getting heads.
On three flips,
HHH HTH HHT HTT TTT THT TTH THH
There's a 7/8 of a chance of getting heads.
The more times you flip, the closer it comes to being a 100% certainty, but it never gets there.
If Buffy was in Vegas 9 days a year, for me to be 100% certain of meeting her, I'd have to be there 357 days.
But if I'm only there four days, are the odds 4/357, or 89-1?
