A bag contains 12 balls of the same shape and size.
Of these, 9 balls are blue, and the remaining 3 balls arered.
Suppose that you do the following iterative random experiment:In each iteration, 5 balls are removed randomly (withoutreplacement) from the bag, in such a way that any 5 balls in thebag are equally likely to be the 5 balls that are removed. Afterdoing this, you check whether among the 5 removed balls there areexactly 2 red balls. If so, then you STOP. Otherwise, you replacethe 5 balls back into the bag, shake the bag up (to make sure it israndomly mixed again), and repeat the same experiment: randomsample 5 balls from the bag, and check whether you have taken outexactly 2 red balls.
You repeat this until the process STOPs (i.e., when the 5removed balls in some iteration contain exactly 2 red balls amongthem).
What is the expected number of times that you will sample 5balls from this bag, in the above random experiment?
