Question

Checking independence Suppose A and B are two events such that$P\left(A\right)=0.3andP\left(B\right)=0.4$, and$P(A\cap B)=0.12$. Are events A and B independent? Justify your answer.

Short answer

Events $A$ and $B$ are independent

Step-by-step solution

Given information

Given,

$$\begin{gathered} P\left(A\right)=0.3,P\left(B\right)=0.4 \\ P(A\cap B)=0.12 \end{gathered}$$

Calculation

Events $A$and $B$are independent if

$P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$

Here,

$P\left(A\right)P\left(B\right)=0.3(0.4)=0.12=P\left(A\cap B\right)$

Therefore, $A$and $B$are independent.