Welcome to the article Nick has 4 black pens 3 blue pens and 2 red pens in his bag Nick randomly picks two pens out of his school bag. 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!
Answer :
Final Answer:
The probability that Nick chooses two blue pens, with replacement, from his bag is [tex]\( \frac{3}{9} \times \frac{3}{9} = \frac{1}{9} \)[/tex] or approximately 0.1111.
Explanation:
When Nick randomly selects a pen from his bag, there are a total of 4 + 3 + 2 = 9 pens. Since he replaces the first pen before choosing the second one, the probabilities are independent. To find the probability of selecting two blue pens, we need to calculate the probability of selecting a blue pen on the first draw and a blue pen on the second draw, and then multiply these probabilities together.
There are 3 blue pens out of 9 total pens, so the probability of choosing a blue pen on the first draw is [tex]\( \frac{3}{9} \).[/tex]
Since Nick replaces the first pen, there are still 3 blue pens out of 9 total pens left. Therefore, the probability of choosing a blue pen on the second draw is also [tex]\( \frac{3}{9} \).[/tex]
To find the combined probability, we multiply the probabilities of both draws:
[tex]\( \frac{3}{9} \times \frac{3}{9} = \frac{9}{81} = \frac{1}{9} \)[/tex], which is approximately 0.1111.
In conclusion, the probability that Nick chooses two blue pens, with replacement, from his bag is [tex]\( \frac{1}{9} \)[/tex] or approximately 0.1111. This probability reflects the independent nature of the two draws and the relative frequency of blue pens in Nick's bag.
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