Direction: Solve the problem below and construct probability distribution and make a histogram. Suppose three cellphones are tested at random. We want to find out the number of defective cellphones that occur. Thus, to each outcome in the sample space we shall assign a value.

Let $D$ represent the defective and $N$ represent non-defective cellphone. Let $X$ be the random variable representing the number of defective cell phones.

Sample space:

$S=\{NNN,NND, NDN,DNN,$

$NDD, DND, DDN,DDD\}$

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

$\def\arraystretch{1.5} \begin{array}{c:c} Possible \ Outcomes & X \\ \hline NNN & 0\\ \hdashline NND & 1 \\ \hdashline NDN & 1 \\ \hdashline DNN & 1 \\ \hdashline NDD & 2 \\ \hdashline DND & 2 \\ \hdashline DDN & 2 \\ \hdashline DDD & 3 \\ \hdashline \end{array}$

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

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

or

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