Question

If $0<P(A)<1,0<P(B)<1$ and $P(A\cap B)=P(A)+P(B)-P(A)P(B)$, then

• A. $P(B/A)=P(B)-P(A)$
• B. $P(A^{\prime }-B^{\prime })=P(A^{\prime })-P(B^{\prime })$
• C. $P(A\cup B{)}^{\prime }=P(A{)}^{\prime }P(B{)}^{\prime }$
• D. $P(A/B)=P(A)-P(B)$

Answer 1

Answer: (B)

Since, $P(A\cap B)=P(A)P(B)$
It means $A$ and $B$ are independent events, so $A$ ' and $B$ ' are also independent.
$\therefore P(A\cup B{)}^{\prime }=P(A^{\prime }\cup B^{\prime })=P(A{)}^{\prime }.P(B{)}^{\prime }$
Alternate Solution
$P(A\cup B{)}^{\prime }=l-P(A\cup B)=1-[P(A)+P(B)-P(A).P(B)$
$=1-P(A)1-P(B)=P(A{)}^{\prime }P(B{)}^{\prime }$