Q.From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when i) first card drawn is kept aside ii) the first card drawn is replaced in the pack.

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. …