A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event “number is even” and B be the event “number is marked red”. Find whether the events A and B are independent or not.

Given : $S=\left \{ 1,2,3,4,5,6 \right \}$

Let two events be $A=\left \{ 2,4,6 \right \}$    The number is even

$B=\left \{ 1,2,3 \right \}$  The number is red

$P(A)=\frac{3}{6}=\frac{1}{2}$

$P(B)=\frac{3}{6}=\frac{1}{2}$

And  $P(A\cap B)=\frac{1}{6}$

Now, $P(A\cap B)=P(A)\cdot P(B)$

Applying the value:     $\frac{1}{6}=\frac{1}{2}\cdot \frac{1}{2}$

$\frac{1}{6}\neq\frac{1}{4}$

$\therefore P(A\cap B)\neq P(A)\cdot P(B)$

Hence, A and B are not independent.

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