Explain why the experiment of tossing a coin three times is said to have Binomial distribution.

We know that, a random variable X taking values $0,1,2, \ldots , n$ is said to have a binomial distribution with parameters $n$ and $P$,

if its probability distribution is given by

$P(X = r){ = ^n}{C_r}{p^r}{q^{n - r}}$

where, $q = 1 - p$
and $r = 0,1,2, \ldots ,n$

Similarly, in an experiment of tossing a coin three times,

we have $n = 3$ and random variable X can take values $r = 0,1,2$ and 3 with $p = \frac{1}{2}$ and $q = \frac{1}{2}$

So, we see that in the experiment of tossing a coin three times,

we have random variable X which can take values 0,1,2 and 3 with parameters $n = 3$ and $P = \frac{1}{2}$.

Therefore, it is said to have a Binomial distribution.