Answer to Question #178601 in Statistics and Probability for Nicolas Flavio

Question #178601

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.

Expert's answer

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

Automobiles can be: 

where  denotes the non-blemished and  denotes the blemished ones.

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

Element of sample space S for X 

Case 1: For 

Sample space will be 

Case 2: For 

Sample space will be:

Case 3: For 

Sample space will be:

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