NDA 2025 Maths · Mathematics · Probability · medium

The events A and B are independent when P(A∩ B)=P(A)P(B). 2. Whenever P(A)>0 and P(B)>0, the conditional probabilities P(Amid B) and P(Bmid A) are…

Single correct option

Consider the following statements:
1. The events

A

and

B

are independent when

P(A\cap B)=P(A)P(B)

.
2. Whenever

P(A)>0

and

P(B)>0

, the conditional probabilities

P(A\mid B)

and

P(B\mid A)

are equal.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) $1$ only

Statement 1 is the definition of independence, so it is correct. For statement 2,

P(A|B)=\frac{P(A\cap B)}{P(B)}

and

P(B|A)=\frac{P(A\cap B)}{P(A)}

, which are equal only if

P(A)=P(B)

(or the intersection is empty). It is not true in general.

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