Question

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

Explanation:

Step1: Calculate probability of faulty pens

The probability of a pen being faulty is $\frac{1}{9}$.

Step2: Calculate probability of drawing a 10 from a standard deck

A standard deck has 52 cards and 4 tens. So the probability of drawing a 10 is $\frac{4}{52}=\frac{1}{13}$.

Step3: Analyze each option

• Option A: Removing hearts doesn't change the ratio of 10s to non - 10s in a meaningful way to match $\frac{1}{9}$.
• Option B: The model can be improved as the current probability of getting a 10 ($\frac{1}{13}$) is not $\frac{1}{9}$.
• Option C: Removing face - cards changes the total number of cards but not in a way to make the probability of getting a 10 equal to $\frac{1}{9}$.
• Option D: A standard deck has 52 cards. After removing 12 face - cards and 4 aces, there are $52-(12 + 4)=36$ cards left. There are still 4 tens. The probability of drawing a 10 from this new deck is $\frac{4}{36}=\frac{1}{9}$.

Answer:

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