Question

Consider the following in respect of two events $A$ and $B$:
(1) $P(A$ occurs but not $B)=P(A)-P(B)$ if $B\subset A$
(2) $P(A$ alone or $B$ alone occurs) $=P\left(A\right)+P\left(B\right)-P(A\cap B)$
(3) $P(A\cup B)=P\left(A\right)+P\left(B\right)$ if $A$ and $B$ are mutually exclusive
Which of the above is/are correct?

• A. 1 only
• B. 1 and 3 only
• C. 2 and 3 only
• D. 1 and 2 only

Answer 1

The correct option is B 1 and 3 only

If $B\subset A$, then $P(A-B)=P\left(A\right)-P(A\cap B)=P\left(A\right)-P\left(B\right)$. Statement 1 is correct.

$P\left(A\text{alone or}B\text{alone}\right)=P\left(A\right)-P(A\cap B)+P\left(B\right)-P(A\cap B)=P\left(A\right)+P\left(B\right)-2P(A\cap B)$Statement 2 is false.

If $A$ and $B$ are mutually exclusive, then $P(A\cap B)=0⟹P(A\cup B)=P\left(A\right)+P\left(B\right)$. Statement 3 is correct.

Hence, answer is 1 and 3 only.