select the correct answer. juan runs a company that makes pens. he notices that 1 out of every 9 pens are…

select the correct answer. 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 can be improved the most by removing all the face cards and aces from the deck. 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 face cards from the deck. d. his model cannot be improved.

select the correct answer. 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 can be improved the most by removing all the face cards and aces from the deck. 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 face cards from the deck. d. his model cannot be improved.

Answer

Answer:

A. His model can be improved the most by removing all the face cards and aces from the deck.

Explanation:

Step1: Calculate original proportion of 10s

In a standard deck of 52 cards, there are 4 cards with the value 10. So the proportion of 10s is $\frac{4}{52}=\frac{1}{13}$.

Step2: Analyze the goal proportion

The proportion of faulty pens is $\frac{1}{9}$.

Step3: Consider card - removal effects

If we remove face - cards (Jack, Queen, King) and aces, there are 52-(12 + 4)=36 cards left. And there are still 4 cards with the value 10. Now the proportion of 10s is $\frac{4}{36}=\frac{1}{9}$, which matches the proportion of faulty pens. Removing hearts or just face - cards does not achieve this match. So the model can be improved by removing face - cards and aces.