Question

A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let A be the event, " the number is even ", and B be the event, " the number is red ". Are A and B independent ?

Answer 1

Even numbers on die are 2, 4, 6.

Therefore, probability of getting even number, $P\left(A\right)=\frac{3}{6}=\frac{1}{2}$

There are two colours of the die - Red and Green

Probability of getting red colour, $P\left(B\right)=\frac{1}{2}$

Even number in red colour is 2.

Therefore, probability of getting red colour and even number = $P(A\cap B)=\frac{1}{6}$

$P\left(A\right).P\left(B\right)=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}\ne \frac{1}{6}\ne P(A\cap B)$

Hence, A and B are not independent.