Solution: Let A be the event that the initial marble is green, B be the event that the removed marble is green, and C be the event that the remaining marble is green. We need to find P(C|B). There are several ways to find this; one natural way is to condition on whether the initial marble is green: P(C|B) = P(C|B,A)P(A|B) + P(C|B,Ac)P(Ac|B) = 1P(A|B) + 0P(Ac|B).
To find P(A|B), use Bayesâ€™ Rule: P(A|B) = P(C|B) = 2/3.

Copyright © 2011 Stat 110 Harvard.
Website layout by former Stat110'er.