Four coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y . Construct a probability distribution.

There are $2^4=16$ possible outcomes

$S=\{HHHH, HHHT, HHTH, HTHH, THHH,$

$HHTT, HTHT, HTTH, THTH, THHT, TTHH,$

$HTTT, THTT, TTHT, TTTH, TTTT\}$

The possible values of the random variable $Y$ are $0, 1, 2, 3, 4.$

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

$p = q =1/2$

Construct the probability distribution of the random variable

$\def\arraystretch{1.5} \begin{array}{c:c} y & 0 & 1 & 2 & 3 & 4 \\ \hline p(y) & 1/16 & 1/4 & 3/8 & 1/4 & 1/16 \end{array}$

or

$\def\arraystretch{1.5} \begin{array}{c:c} y & 0 & 1 & 2 & 3 & 4 \\ \hline p(y) & 0.0625 & 0.25 & 0.375 & 0.25 & 0.0625 \end{array}$