Juan runs a company that makes pens. He notices that 1 out of every 9 pens are faulty. He uses a standard deck of cards to model the situation, with all the 10s representing faulty pens. Which statement about his model is true?

A.
His model cannot be improved.
B.
His model can be improved the most by removing all the hearts from the deck.
C.
His model can be improved the most by removing all the face cards and aces from the deck.
D.
His model can be improved the most by removing all face cards from the deck.

Question

Juan runs a company that makes pens. He notices that 1 out of every 9 pens are faulty. He uses a standard deck of cards to model the situation, with all the 10s representing faulty pens. Which statement about his model is true?

A. 
His model cannot be improved.
B. 
His model can be improved the most by removing all the hearts from the deck.
C. 
His model can be improved the most by removing all the face cards and aces from the deck.
D. 
His model can be improved the most by removing all face cards from the deck.

SmokeyBrown · Answer

Let's take a look at the model Juan made and compare it to what he's trying to represent.

In Juan's model, all of the 10s represent faulty pens. In a normal deck of cards, there are 13 total card values, so the model would actually represent 1/13 pens being faulty. Now, Juan *actually* wants to represent 1/9 pens being faulty.

So, which of the choices is an improvement that would let Juan more accurately represent the 1/9 chance?