Q.A box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, a) the first is red and the second is green? b) one is red and the other is green?

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. …