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NIMCET 2026 — Mathematics PYQ

NIMCET | Mathematics | 2026

Let $A_{1}, A_{2}, A_{3}$ are three events in a sample space with the condition: $A_{1} \cap A_{2} \neq = \emptyset$ , then always

Choose the correct answer:

Explanation

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:

$P (A_{1} \cap A_{2} \cap A_{3}) = P (A_{1}) \cdot P (\frac{A _{2}}{A _{1}}) \cdot P (\frac{A _{3}}{A _{1} \cap A _{2}})$

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

Correct Option: (b)

If a number $x$ is selected at random from natural numbers 1,2,……,100,then …

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