Help with compound probability computation, please!
MicroTech
10 buckets, each numbered from 0 to 9.
A large supply of balls, each randomly numbered from 0 to 9. The
supply will not run out.
Procedure:
GO: REPEAT: Pick a random (p=1/10) ball and throw it at the row of
buckets. There are n empty buckets, and the ball always lands in a
random (p=1/n) empty bucket.
If any bucket is still empty, go to REPEAT.
Remove all balls that did not land in its designated bucket (ball # <>
bucket #).
If any bucket is still empty, go to GO.
Now all 10 buckets n contains ball n (n = 0 to 9).
Question 1: How do I compute the probability for getting all balls
into their designated bucket (ball # = bucket #) in n repetitions of
the procedure (passing GO)?
Question 2: Is there a general formula that gives "With n repetitions
of the procedure (passing GO), the probability of getting all ten
buckets to contain its designated ball is x"?
Help would be much appreciated!
Henry Norman