Mathematics

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.}

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

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

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