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 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 hearts 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 face cards and aces 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 hearts from the deck.

Answer

Explanation:

Step1: Calculate probability of faulty pens

The probability that a pen is faulty is $\frac{1}{9}$. In a standard deck of 52 cards, there are 4 tens. So the probability of drawing a ten from a standard deck is $\frac{4}{52}=\frac{1}{13}$.

Step2: Analyze option A

If we remove all face - cards (12 cards) and aces (4 cards) from the deck, we are left with $52-(12 + 4)=36$ cards. There are still 4 tens. The new probability of drawing a ten is $\frac{4}{36}=\frac{1}{9}$, which matches the probability of a faulty pen.

Step3: Analyze option B

As shown in step 2, the model can be improved, so this option is incorrect.

Step4: Analyze option C

If we remove only face - cards (12 cards), we have $52 - 12=40$ cards. The probability of drawing a ten is $\frac{4}{40}=\frac{1}{10}\neq\frac{1}{9}$.

Step5: Analyze option D

If we remove all hearts (13 cards), we have $52-13 = 39$ cards. The probability of drawing a ten is $\frac{4}{39}\neq\frac{1}{9}$.

Answer:

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