Question

If $P\left(A\right)=0.3$, $P\left(B\right)=0.4$, then the value of $P(A\cup B)$ where $A$ and $B$ are independent events is

• A. $0.48$
• B. $0.51$
• C. $0.52$
• D. $0.58$

Answer 1

The correct option is D $0.58$

If $A$ and $B$ are two independent events, then $P(A\cap B)=P\left(A\right)P\left(B\right)$

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

$⟹P(A\cup B)=0.3+0.4-\left(0.3\right)\left(0.4\right)$ ....... $[\because P(A\cap B)=P(A)\cdot P(B\left)\right]$

$⟹P(A\cup B)=0.58$