Question

Construct the probability distribution of a particular experiment by following the instructions given to you.

A dog gave birth to a litter of six puppies. Three of them are male while the rest are female.if you are to be given three of these puppies at random,list all the elements of the sample space using the letters M and F for male puppies band female puppies, respectively.then assign a value x of the random variable X representing the number..

Possible Outcomes/Value of Random Variable X

Answer 1

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

Sample space S is all possible outcomes of three puppies.

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

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

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

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

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