Welcome to the article A bag contains 3 blue pens and 5 red pens If two pens are taken out of the bag randomly with replacement one at a. 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 :
To solve this problem, we need to find the probability that two pens drawn, one at a time with replacement, are of different colors. Here's how to approach it step-by-step:
1. Understand the Setup:
- We have a total of 8 pens: 3 blue and 5 red.
- Since we are drawing with replacement, the total number of pens remains constant for each draw.
2. Calculate the Probability of Each Scenario:
- Scenario 1: Pick a blue pen first and a red pen second.
- Probability of picking a blue pen first is [tex]\( \frac{3}{8} \)[/tex].
- Since it's with replacement, the probability of picking a red pen second is [tex]\( \frac{5}{8} \)[/tex].
- Thus, the probability for the scenario is:
[tex]\[
\frac{3}{8} \times \frac{5}{8} = \frac{15}{64} \approx 0.234375
\][/tex]
- Scenario 2: Pick a red pen first and a blue pen second.
- Probability of picking a red pen first is [tex]\( \frac{5}{8} \)[/tex].
- Again, since it's with replacement, the probability of picking a blue pen second is [tex]\( \frac{3}{8} \)[/tex].
- Thus, the probability for this scenario is:
[tex]\[
\frac{5}{8} \times \frac{3}{8} = \frac{15}{64} \approx 0.234375
\][/tex]
3. Combine the Probabilities:
- To find the probability that the two pens are of different colors, we add the probabilities of the two scenarios:
[tex]\[
\frac{15}{64} + \frac{15}{64} = \frac{30}{64} = \frac{15}{32} \approx 0.46875
\][/tex]
The probability that the two pens drawn are of different colors is approximately 0.46875.
1. Understand the Setup:
- We have a total of 8 pens: 3 blue and 5 red.
- Since we are drawing with replacement, the total number of pens remains constant for each draw.
2. Calculate the Probability of Each Scenario:
- Scenario 1: Pick a blue pen first and a red pen second.
- Probability of picking a blue pen first is [tex]\( \frac{3}{8} \)[/tex].
- Since it's with replacement, the probability of picking a red pen second is [tex]\( \frac{5}{8} \)[/tex].
- Thus, the probability for the scenario is:
[tex]\[
\frac{3}{8} \times \frac{5}{8} = \frac{15}{64} \approx 0.234375
\][/tex]
- Scenario 2: Pick a red pen first and a blue pen second.
- Probability of picking a red pen first is [tex]\( \frac{5}{8} \)[/tex].
- Again, since it's with replacement, the probability of picking a blue pen second is [tex]\( \frac{3}{8} \)[/tex].
- Thus, the probability for this scenario is:
[tex]\[
\frac{5}{8} \times \frac{3}{8} = \frac{15}{64} \approx 0.234375
\][/tex]
3. Combine the Probabilities:
- To find the probability that the two pens are of different colors, we add the probabilities of the two scenarios:
[tex]\[
\frac{15}{64} + \frac{15}{64} = \frac{30}{64} = \frac{15}{32} \approx 0.46875
\][/tex]
The probability that the two pens drawn are of different colors is approximately 0.46875.
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Rewritten by : Brahmana