Question

If M and N are any two events, the probability that not exactly one of them occurs is for an event set A, the complement is $A^o$.

• A. $P\left(M\right)+P\left(N\right)-2P(M\cap N)$
• B. $P\left(M\right)+P\left(N\right)-P(M\cap N)$
• C. $P\left(M^o\right)+P\left(N^o\right)-2P(M^o\cup N^o)$
• D. $P(M\cap N^o)+P(M^o\cup N)$

Answer 1

The correct option is A $P\left(M\right)+P\left(N\right)-2P(M\cap N)$

$P\left(\text{Exactly one occur}\right)=P\left(M\right)+P\left(N\right)-P(M\cap N)-P(N\cap M)$
$\therefore P(M\cap N)=P(N\cap M)$
$=P\left(M\right)+P\left(N\right)-2P(M\cap N)$