Not sure if I did part a correctly. Part B, not even sure how to do it.
A bin contain balls numbered 1 through 5. Balls are removed, one at a time, until a ball with a similar value tan the previous number is drawn.
a. Find the probability that you stop after three draws (the third ball has a smaller value)
I first figured that there were 14 possible formations that would meet the requirements. They are:
(2,3,1), (2,4,1), (2,4,3), (2,5,1), (2,5,3), (2,5,4), (3,4,1), (3,4,2), (3,5,1), (3,5,2), (3,5,4), (4,5,1), (4,5,2), (4,5,3)
I then figured out the total possible formations 5P3 = 60
14/60 = .2333 is the probability that I would stop after three draws. Was I correct in completing this problem?
b. Let X represent the value of the ball that is the first ball with a smaller value. Determine the probability mass function on X.