What are the odds of this happening? There is a list of exactly 94 names on it. One person randomly picks 5 names on the list and doesn't show them to anyone. Another person picks just 2 names on the list. What are the odds that one of the names they both picked is a match?
This has happened to me more than once and I'm curious what the odds are.
 A: If it's an event specified after the fact, the probability calculation isn't particularly meaningful (what's the probability of this thing I just saw? suffers from the problems of any data-generated hypothesis  - we don't know what else might have led you to ask the same question). 
But if we're talking about what the probability is that you'll see it on the next experiment, that would be a calculation we can make.
Let's also (unrealistically) assume that the 'random' choice really is made randomly.
Let's take as a model for your problem that a deck of 94 unique cards is shuffled so that all orders of cards are equally likely (which we'll call "perfectly shuffled"), and then the top 5 are drawn, and then the deck is again perfectly shuffled and the top two cards are drawn.
Consider the complementary event of the desired one -- none of the two cards in the second draw match the previous five drawn. We consider this because it's relatively simple to calculate.
Look at the first of the two cards. There are 94 cards to choose from and 89 of them don't match any in the previous draw of five ($\frac{_{89}}{^{94}}$). If it didn't match any of the five, the second card has probability $\frac{_{88}}{^{93}}$ of no match.
So the probability that none of the two cards in the second draw match any of the previous five is $1-\frac{_{89}}{^{94}}\cdot\frac{_{88}}{^{93}}$.
