Question

If $P\left(A\right)=0.7$, $P\left(B\right)=0.4$, then the interval in which $P(A\cap B)$ lies is

• A. $[0.1,0.4]$
• B. $[0.1,0.6]$
• C. $[0,0.4]$
• D. None of these

Answer 1

The correct option is C $[0,0.4]$

$P\left(A\right)=0.7,P\left(B\right)=0.4$

Minimum value of $P(A\cap B)=0$ (when $A$ and $B$ are disjoint)

Maximum value of $P(A\cap B)=P\left(B\right)=0.4$

$\therefore P(A\cap B)\in [0,0.4]$