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

The overseas shipment has 5 automobiles out of which 2 have slight paint blemishes.

Automobiles can be: $[N_1,N_2,N_3,B_1,B_2]$

where $N_i's$ denotes the non-blemished and $B_i's$ denotes the blemished ones.

Let X be the number of automobiles purchased with paint blemishes.

Element of sample space S for X $=0,1,2$

Case 1: For $X=0$

Sample space will be $(N_1,N_2,N_3)$

Case 2: For $X=1$

Sample space will be:

$[(N_1,N_2,B_1),(N_1,N_2,B_2),(N_1,N_3,B_1),\\ (N_1,N_3,B_2),(N_3,N_2,B_1),(N_3,N_2,B_2)]$

Case 3: For $X=2$

Sample space will be:

$[(N_1,B_1,B_2),(N_2,B_1,B_2),(N_3,B_1,B_2)]$