Answer to Question #305362 in Statistics and Probability for Adrian

Question

Suppose three coins are tossed. Let Y be the random variable representing the number of heads that occur. Find the probability of each of the values of the random variable Y completele the table below

Answer 1

Let's denote $H$ - heads, $T$ - tails.

There are $2^3=8$ possible outcomes

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

$$HTT, THT, TTH, TTT\}$$

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

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

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

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

or

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