geeks who eat...

Anyone who's ever sat through any theoryCS conference lunch/dinner knows that as the meal wears on, the probability that someone will make some silly joke about dining philosophers tends to one.

I am therefore gratified to see the possible emergence of another dining problem in a different community, in this case statistics:

2 groups of statisticians want to lunch together, but have managed to travel to 2 different restaurants. There is a third similar restaurant nearby. In fact the 3 restaurants are equidistant; it takes exactly 5 minutes to move from one to another. The statisticians have dashed to lunch without their cellphones, and don't know the phone numbers for any of the restaurants, so they can't communicate. Having a shocking faith in randomness, they have devised a technique for joining up. Each group will wait a random time--exponentially distributed with a mean of 5 minutes--and then move to another restaurant, selected randomly (of course) with a coin toss. They either meet, or repeat the process. What is the probability that one group will meet the other after moving only once?