three coins are tossed let h be the random variable when head will occur.find the values of the random variable H

There are $2^3=8$ possible outcomes

$S=\{HHH, HHT, HTH, THH,$

$HTT, THT, TTH, TTT\}$

The possible values of the random variable $H$ are $0, 1, 2, 3.$

We will assume that the probability of getting heads and tails is the same:

$p = q =1/2$$\def\arraystretch{1.5} \begin{array}{c:c} Possible \ Outcomes & H \\ \hline HHH & 3 \\ \hdashline HHT & 2 \\ \hdashline HTH & 2 \\ \hdashline THH & 2 \\ \hdashline HTT & 1 \\ \hdashline THT & 1 \\ \hdashline TTH & 1 \\ \hdashline TTT & 0 \\ \hdashline \end{array}$

Construct the probability distribution of the random variable

$\def\arraystretch{1.5} \begin{array}{c:c} h & 0 & 1 & 2 & 3 \\ \hline p(h) & 1/8 & 3/8 & 3/8 & 1/8 \end{array}$

or

$\def\arraystretch{1.5} \begin{array}{c:c} h & 0 & 1 & 2 & 3 \\ \hline p(h) & 0.125 & 0.375 & 0.375 & 0.125 \end{array}$