Alright, let me throw a wrench into things by looking at it another way!
By the way, plaw, I think you 4/357 was good. It works for me.
Anyway, here's my thought... Why don't we look at it from the converse... Figure out what the probability of never meeting Buffy on any of the 4 days plaw is there. Knowing that probability, we can subtract it from 1 and that will be the probability of meeting Buffy.
Anyway, say it's plaw's first day at Vegas, he just got off the plane rarin' to go. He checks into his hotel and immediately makes a beeline to the nearest $8/$4 poker table...
The probability of not meeting Buffy the first day is 356/365 (Buffy is not there 356 days in a year).
The second day, plaw is tired from the 4 hours of more poker and has had his fill with the $4 Steak and Lobster Buffet. He decides he wants to watch Celine Dion.
The prob of not meeting Buffy is 355/364 since we know that he didn't meet her the first day.
It's plaw's third day. He's up $2000 and feeling frisky. He heads over to the nearest gentleman's club and proceeds to stay there for 3 hours. He is now down $500, but very, very happy!
The prob of not meeting Buffy: 354/363.
4th day. Plaw wants to recoup his losses from the night before. He heads over to the blackjack table and employs a little basic strategy. Face cards are -1, low cards +1. He's having a good time, splitting face cards, doubling down and before he realizes, he needs to catch a cab for the airport. He tips the waitress a $100 chip and walks away knowing he made $200 that weekend. Sadly, he never met Buffy.
Prob he didn't meet Buffy the 4th day...353/362.
Therefore, the probability of not meeting her in any of the 4 days is a case of conditional probability (e.g. prob of not meeting her 2nd day is dependent on the fact that he didn't meet her the first day; third day dependent on 1st and 2nd day, etc)
The probability of not meeting her then is
356/365 * 355/364 * 354/363 * 353/362 = 90.5%
Therefore, the probability of meeting Buffy on any of the four days is approximatley 10%.
