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Welcome to the article A bag contains 3 red pens 7 blue pens and some black pens If a pen is picked randomly from the bag the probability of. 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 bag contains 3 red pens, 7 blue pens, and some black pens. If a pen is picked randomly from the bag, the probability of picking a red pen is [tex]\frac{1}{6}[/tex]. What is the number of black pens?

A. 3
B. 6
C. 8
D. 10

Answer :

To answer the question, we need to determine the number of black pens in the bag.

Given:
- Number of red pens = 3
- Number of blue pens = 7
- Probability of picking a red pen = [tex]\(\frac{1}{6}\)[/tex]
- Let the number of black pens be [tex]\(x\)[/tex]

The total number of pens in the bag is the sum of red, blue, and black pens. Therefore, the total number of pens is:
[tex]\[ \text{Total number of pens} = 3 + 7 + x = 10 + x \][/tex]

The probability of picking a red pen is given by the ratio of the number of red pens to the total number of pens. Therefore, we have the following equation for the probability:
[tex]\[ \frac{3}{10 + x} = \frac{1}{6} \][/tex]

Next, we solve this equation to find the value of [tex]\(x\)[/tex]:
1. Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[ 3 \cdot 6 = (10 + x) \cdot 1 \][/tex]
[tex]\[ 18 = 10 + x \][/tex]

2. Isolate [tex]\(x\)[/tex] by subtracting 10 from both sides of the equation:
[tex]\[ 18 - 10 = x \][/tex]
[tex]\[ x = 8 \][/tex]

So, the number of black pens is [tex]\(8\)[/tex]. Thus, the correct answer is:
[tex]\[ \boxed{8} \][/tex]

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Rewritten by : Brahmana