Solution: Let A = the event that the first marble is black; and let B = the event that the second marble is black. We know the following:
In the beginning, there are 10 marbles in the urn, 4 of which are black. Therefore, P(A) = 4/10.
After the first selection, there are 9 marbles in the urn, 3 of which are black. Therefore, P(B|A) = 3/9.
Therefore, based on the rule of multiplication:
P(A ∩ B) = P(A) P(B|A)
P(A ∩ B) = (4/10)*(3/9) = 12/90 = 2/15