NDA 2020 Maths · Mathematics · Probability · medium

For events A and B: 1. If A and B are mutually exclusive and both have non-zero probability, they cannot be independent. 2. P(A∪ B)=P(A)+P(B) for any…

Single correct option

Consider the following statements for events

A

and

B

:
1. If

A

and

B

are mutually exclusive and both have non-zero probability, they cannot be independent.
2.

P(A\cup B)=P(A)+P(B)

for any two events

A

and

B

.
Which of the statements is/are correct?

Show answer and solution

Answer: (A) 1 only

A\cap B=\varnothing

then

P(A\cap B)=0

, but independence needs

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

when both are non-zero. These conflict, so such events cannot be independent: statement 1 is correct. Statement 2 omits the term

-P(A\cap B)

; the formula holds only for mutually exclusive events. For example, with a die,

A=\{2,4,6\}

and

B=\{1,2\}

give

P(A\cup B)=\tfrac46\ne\tfrac36+\tfrac26

Original question written in the NDA 2020 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