Answer to Question #315232 in Statistics and Probability for MAE

Question

Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with paint blemishes. Hint: There are eight (8) elements in the sample space. 

Answer 1

Actually there 7, not 8 elements in the sample space.

As there are two blemished automobiles, the number ot them X among the three purchased ones, can take on values 0, 1, 2 (there are 5 - 2 = 3 non-blemished automobiles); X = 3 is an impossible value.

The sample space:

$S = \begin{Bmatrix} NNN, NNB, NBN, BNN, BBN, BNB, NBB\end{Bmatrix}.$

With each sample point we'll associate a value of the random variable X:

$NNN\qquad X=0\\NNB\qquad X=1\\NBN\qquad X=1\\BNN\qquad X=1\\ BBN\qquad X=2\\BNB\qquad X=2\\NBB\qquad X=2$