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". State whether $A$ and $B$ are independent events or not.

Answer 1

We have, $A=\{2,4,6\}B=\{1,2,3\}andA\cap B=\left\{1\right\}$

$\therefore P\left(A\right)=\frac{3}{6}=\frac{1}{2},P\left(B\right)=\frac{3}{6}=\frac{1}{2}$ and $P(A\cap B)=\frac{1}{6}$.

Clearly, $P(A\cap B)\ne P\left(A\right)P\left(B\right)[As\frac{1}{6}\ne \frac{1}{2}\times \frac{1}{2}]$

So, $A$ and $B$ are not independent events.