For two events and in a sample space,

MATHEMATICS · Single correct · CBSE · Mathematics · Probability · Probability

Problem

For two events

A

and

B

in a sample space,

P(A)=0.5

P(B)=0.4

and

P(A\cup B)=0.9

. Which one of the following statements is true? (a)

P(A\cap B)=0.9,\;\text{so }A\text{ and }B\text{ are identical events.}

(b)

P(A\cap B)=0.2,\;\text{assuming }A\text{ and }B\text{ are independent.}

(c)

P(A\cap B)=0,\;\text{so }A\text{ and }B\text{ are mutually\;exclusive.}

(d)

P(A\cap B)=0.1,\;\text{so }A\text{ and }B\text{ overlap.}