An urn contains 3 red balls and 3 green balls. A ball is drawn randomly. If red, kept out. If green, returned to urn. Second ball is drawn, repeat. What is the probability that the urn contains exactly 4 balls after 3 are drawn?
This is exactly as asking what's the probbly of drawing exactly 2 red balls in three intents. Let us denote the ball drawn in the i-th intent.
We have the following drawings that'll give 4 balls after 3 drawings:
Now evaluate each event's probability. For example, in the first event the probability is ...can you see why?