We have an urn with two yellow and 3 green balls. We choose a ball randomly, look at its color and return it into the urn with an extra ball of the same color. We repeat this step two more times (in the end there are 8 balls in the urn).
(a) What is the probability that the three balls chosen in the three steps are of the same colors?
(b) What is the probability that we chose a green ball in the second step?
(c) What is the conditional probability that last ball we chose is green given that the first chosen ball was yellow?