Q.An urn contains 4 black, 5 white and 6 red balls. Two balls are drawn one after the other without replacement. What is the probability that at least one of them is black?

Step 1 — State the theorem

The compound probability theorem expresses the joint probability of two events occurring together:

Option (A) matches this exactly.

Step 2 — Why the others fail

(C) $P(A\cap B)=P(A)\times P(B)$ holds only when A and B are INDEPENDENT — a special case, not the general theorem. (D) $P(A\cup B)=P(A)+P(B)-P(A\cap B)$ is the ADDITION theorem for a union. (B) mixes a union with a conditional probability, which is meaningless. …