Question

If $P\left(A\right)=65,P\left(B\right)=80$, then $P(A\cap B)$ lies in the interval

• A. $[.30,.80]$
• B. $[.35,.75]$
• C. $[.4,.70]$
• D. $[.45,.65]$

Answer 1

The correct option is D $[.45,.65]$

$P(A\cap B)\le min\left\{P\right(A),P(B\left)\right\}=min\{.65,.80\}=0.65$

$\therefore P(A\cap B)\le .65$

Also, $P(A\cap B)=P\left(A\right)+P\left(B\right)-P(A\cup B)$

$\ge .65+.80-1=0.45$

$\therefore 0.45\le P(A\cap B)\le 0.65$.