Answer to Question #307339 in Statistics and Probability for Ayeeshaaaa

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

Answer 1

As there are two automobiles with paint blemishes, the number of the bought blemished cars can take on values 0, 1, 2 (there are 5 - 2 = 3 non-blemished automobiles among the total amount, so all the three received ones can be non-blemished). The order of blemished and non-blemished automobiles doesn't matter, the sample space is

$$S = \begin{Bmatrix} NNN, BNN, BBN \end{Bmatrix}.$$

To the sample point NNN will correspond the value of the random variable X = 0; to the BNN: X = 1 and to the BBN: X = 2.