NDA 2018 Maths · Mathematics · Statistics · medium

Two mutually exclusive events, each with non-zero probability, can be independent. 2. For all events A and B, P(A∩ B)=P(A)P(B).

Single correct option

Consider the following statements:
1. Two mutually exclusive events, each with non-zero probability, can be independent.
2. For all events

A

and

B

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

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

Show answer and solution

Answer: (D) Neither 1 nor 2

A,B

are mutually exclusive then

P(A\cap B)=0

, while independence needs

P(A\cap B)=P(A)P(B)>0

for non-zero probabilities, so statement 1 is false. Statement 2 holds only for independent events, not for all events. Hence neither is correct.

Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake