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Welcome to the article A box contains 6 red pens and 4 blue pens Cory randomly picks a pen from the box and keeps it Then Todd randomly picks. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!

A box contains 6 red pens and 4 blue pens. Cory randomly picks a pen from the box and keeps it. Then Todd randomly picks a pen from the box. What is the probability that both boys will pick red pens?

A. [tex]\frac{1}{3}[/tex]
B. [tex]\frac{9}{25}[/tex]
C. [tex]\frac{1}{30}[/tex]
D. [tex]\frac{1}{36}[/tex]

Answer :

To find the probability that both Cory and Todd will pick red pens, let's follow these steps:

1. Determine the initial total number of pens:
- There are 6 red pens and 4 blue pens in the box.
- So, the total number of pens initially is [tex]\(6 + 4 = 10\)[/tex].

2. Calculate the probability that Cory picks a red pen:
- Cory can choose from all 10 pens, and 6 of them are red.
- Therefore, the probability that Cory picks a red pen is [tex]\(\frac{6}{10} = 0.6\)[/tex].

3. Adjust the totals after Cory picks a red pen:
- If Cory takes one red pen, there will now be 5 red pens left.
- The total number of pens will be [tex]\(10 - 1 = 9\)[/tex].

4. Calculate the probability that Todd also picks a red pen:
- Todd now can pick from the remaining 9 pens, 5 of which are red.
- Thus, the probability that Todd picks a red pen is [tex]\(\frac{5}{9} \approx 0.5556\)[/tex].

5. Determine the probability that both boys pick red pens:
- The probability that both Cory and Todd pick red pens is the product of their individual probabilities:
- [tex]\(0.6 \times 0.5556 = 0.3333\)[/tex].

6. Express the probability as a fraction:
- The probability calculated above, [tex]\(0.3333\)[/tex], corresponds to the fraction [tex]\(\frac{1}{3}\)[/tex].

So, the probability that both boys will pick red pens is [tex]\(\frac{1}{3}\)[/tex]. Therefore, the correct answer is:

A [tex]\(\frac{1}{3}\)[/tex]

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Rewritten by : Brahmana