NIMCET 2025 — Mathematics PYQ

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Question

NIMCET 2025 — Mathematics PYQ

NIMCET | Mathematics | 2025

Let $E$ and $F$ be two events such that $P(E)>0$ and $P(F)>0$ . Which one of the following is NOT equivalent to the condition that $P(E)=P(E/F)$ ?

Choose the correct answer:

Explanation

Solution:

Given: $P(E) = P(E/F)$

This means $E$ and $F$ are Independent Events.

1. For Option (B):

P(E/F) = \frac{P(E \cap F)}{P(F)}

P(E) = \frac{P(E \cap F)}{P(F)}

P(E \cap F) = P(E)P(F)

(Equivalent)

2. For Option (A):

P(F/E) = \frac{P(E \cap F)}{P(E)}

P(F/E) = \frac{P(E)P(F)}{P(E)} = P(F)

(Equivalent)

3. For Option (C):

If $E, F$ are independent, $E^c, F^c$ are also independent.

P(E^c/F^c) = \frac{P(E^c \cap F^c)}{P(F^c)} = \frac{P(E^c)P(F^c)}{P(F^c)} = P(E^c)

(Equivalent)

4. For Option (D):

P(E/F) = P(E)

P(F/E) = P(F)

$P(E/F) = P(F/E)$ only if $P(E) = P(F)$ .

Correct Option: (D)