Answer to Question #300355 in Statistics and Probability for kylle

Question

A dog gave birth of six puppies. Three of them are male while the rest are female. If you are to be

given three puppies at random, list all the elements of the sample space using the letters M and F for

male puppies and female puppies, respectively. Then assign a value x of the random variable X

representing the number of male puppies you receive.

Answer 1

A. Let's denote $M$ - male puppies, $F$ - female puppies.

Sample space S is all possible outcomes of three puppies.

$$S = \{MMM, FMM, MFM, MMF,$$

$$FFM, FMF, MFF, FFF\}$$

B. Let $x$ be the random variable representing the number of male puppies we receive. The possible values of $x$ are $0,1,2,3.$

C.

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ point & y \\ \hline MMM & 3 \\ \hdashline FMM & 2 \\ \hdashline MFM &2 \\ \hdashline MMF & 2 \\ \hdashline FFM & 1 \\ \hdashline FMF & 1 \\ \hdashline MFF & 1 \\ \hdashline FFF & 0 \\ \hdashline \end{array}$$

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