A fair coin is tossed five times repeatedly. Let $A$ be the event in which the number of heads that appeared is at least 2 and $B$ the event in which the number of tails that appeared is at least 2.
Find whether the events $A$ and $B$ are independent.
So far I took $p$ as the probability of heads appearing in a single toss. Then $p= 0.5$. Since this is tossed 5 times(i.e. $n=5$)
\begin{align}P(A)=P(H\geq 2)&=1-[P(H=0)+P(H=1)]\\ &=1-\Big[\binom{5}{0}\cdot 0.5^5 + \binom{5}{1} \cdot 0.5\cdot0.5^4\Big]\\ &= 0.8126 \end{align} In the same manner $P(B)$ can be derived as $0.8126$
To show those events are independent how to proceed?