An Urn contains 5 red, 4 white, and 3 green balls. The experiment E is as follows: draw 3 balls (at random) one at a time, WITH replacement of the ball in the urn after each draw. Each outcome is an ordered triplet of the form (First ball, Second ball, Third Ball).

Let A: "The second and third balls are the same color"

Let B: "The first and third balls are the same color?

Let S be the sample space.

i) Find P(S), P(A), P(B), and P(A n B) - read as probability of intersection of A and B.

ii) Does knowing B has occurred increase the chances that A has also occurred?

i) For P(S) I got 1. I am stuck on the rest of the probabilities

ii) I believe the answer is No, but I am not sure how true my logic is. I feel like since there is replacement, other events already occurring does not increase the likelihood of other events.