Answer to Question #305559 in Statistics and Probability for Luna Heart

Question

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.

Answer 1

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

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