NIMCET 2026 — Mathematics PYQ

To find the probability of the intersection of three events $A_1,A_2,$ and $A_3$, we use the General Multiplication Rule of probability.

The probability of the intersection of multiple events is given by the product of the probability of the first event and the conditional probabilities of the subsequent events, given that the preceding events have already occurred.

The formula is:

$$P(A_1\cap A_2\cap A_3)=P(A_1)\cdot P\left(\frac{A_2}{A_1}\right)\cdot P\left(\frac{A_3}{A_1\cap A_2}\right)$$

Comparing this to the given options, we see that option (b) correctly represents this chain rule of probability.

Correct Option: (b)