Question

If $A$ and $B$ are independent events of a sample space such that $P\left(A\right)=0.2,P\left(B\right)=0.5,$ then which of the following(s) is(are) correct?

• A. $P\left(A/B\right)=0.2$
• B. $P(A\cap B)=0.1$
• C. $P\left(B/A\right)=0.3$
• D. $P(A\cup B)=0.6$

Answer 1

Answer: (A), (B), (D)

$P(A\cup B)=0.6$

As $A$ and $B$ are independent events.
$P\left(A/B\right)=P\left(A\right)=0.2P\left(B/A\right)=P\left(B\right)=0.5P(A\cap B)=P\left(A\right)\cdot P\left(B\right)=0.1$
Now,
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)=0.6$