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 hearts from the deck. b. his model cannot be improved. 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.

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 hearts from the deck. b. his model cannot be improved. 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.

Answer

Answer:

D. His model can be improved the most by removing all face cards from the deck.

Explanation:

Step1: Analyze probability in model

In a standard deck of 52 cards, there are 4 tens (representing faulty pens). The probability of drawing a ten is $\frac{4}{52}=\frac{1}{13}$. We want a probability of $\frac{1}{9}$.

Step2: Consider card - removal effects

Removing face - cards (Jack, Queen, King) reduces the number of non - ten cards. There are 12 face - cards in a deck. After removing face - cards, the new deck has $52 - 12=40$ cards. The probability of drawing a ten becomes $\frac{4}{40}=\frac{1}{10}$, which is closer to $\frac{1}{9}$ than the original $\frac{1}{13}$.

Step3: Analyze other options

Removing hearts (13 cards) doesn't specifically target the probability of getting a ten. Removing face - cards and aces (12 + 4 = 16 cards) makes the probability $\frac{4}{52-(12 + 4)}=\frac{4}{36}=\frac{1}{9}$, but we are looking for the change that improves the model the most incrementally. Just removing face - cards gets us closer to $\frac{1}{9}$ in a more straightforward way compared to removing aces as well.