NDA 2017 Maths · Mathematics · Probability · medium

Examine the following assertions about any two events A and B of a sample space: 1. P(A∪ B)≤ P(A)+P(B). 2. P(A∩ B)≥ P(A).

Single correct option

Examine the following assertions about any two events

A

and

B

of a sample space:
1.

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

.
2.

P(A\cap B)\ge P(A)

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

Show answer and solution

Answer: (A) $1$ only

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

and

P(A\cap B)\ge0

, so the union never exceeds the sum. 2: since

A\cap B\subseteq A

, we always have

P(A\cap B)\le P(A)

; the inequality is reversed. Only assertion 1 is correct.

Original question written in the NDA 2017 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