Question

A fair coin and unbiased die are tossed . Let A be the event 'head appears on the coin' and B be event '3 on the die ' Check whether A and B are independent events or not .

Answer 1

$P\left(A\right)=\frac{6}{12}=\frac{1}{2}\left\{\right(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6\left)\right\}$
$P\left(B\right)=\frac{2}{12}=\frac{1}{6}$
$P(A\cap B)=\frac{1}{12}$
$P\left(A\right)\times P\left(B\right)=\frac{1}{2}\times \frac{1}{6}=\frac{1}{12}=P(A\cap B)$