Sal Baxamusa at The Hardball Times has found that the probability of first hits in a game is about what you would expect when you use the formula:
PROB = (AVG)*(1-AVG)N-1 where N is the out before which the hit happens and AVG is a teams composite average. The hitters do a little better than expected the third time they see a pitcher with a no-hitter in a game.
The fact that it so closely follows the expected probability could lead to some fun questions in finite math class.
When should you start paying to no-hitter to get a 50-50 chance of seeing a no-hit finish?
How many games a season will a team typically not have a hit until the 4th? 5th? 6th?
What is the probability of a game being a no-hitter? How many no-hitters would you expect in a typical MLB season?