Question

Addition Theorem of Probability states that for any two events $A$ and $B$,

• A. $P(A$ $\cup$ $B)=P(A)+P(B)$
• B. $P(A$ $\cup$ $B)=P(A)+P(B)+P(A$ $\cap$ $B)$
• C. $P(A$ $\cup$ $B)=P(A)+P(B)-P(A$$\cap$ $B)$
• D. $P(A$ $\cup$ $B)=P(A)\times P(B)$

Answer 1

Answer: (C)

$P(A$ $\cup$ $B)=P(A)+P(B)-P(A$$\cap$ $B)$

For Addition theorem,

If $A$ and $B$ are any two events associated with a random experiment, then

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

Hence, the answer is $P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B).$