Question

A die, whose faces are marked $1,2,3$ in red and $4,5,6$ in green, is tossed. Let $A$ be the event "number obtained is even" and $B$ be the event "number obtained is red". Find if $A$ and $B$ are independent events.

Answer 1

$A=\{2,4,6\}$

$B=\{1,2,3\}$

$A\cap B=\left\{2\right\}$

$P(A\cap B)=1/6$

$P\left(A\right)=\frac{1}{2}$

$P\left(B\right)=\frac{1}{2}$

$P\left(A\right)P\left(B\right)=\frac{1}{4}\ne P(A\cap B)$

So $A$ and $B$ are independent events.