Welcome to the article A box contains pens Some pens have ink and some do not A teacher randomly selects a pen and sets it aside Then another random. 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 the problem, we need to calculate the probabilities for two sequential events involving selecting pens at random:
1. Event A: The first selection is a pen with ink.
2. Event B: The second selection is a pen with no ink, given that the first was a pen with ink.
Let's break down the solution step by step:
### Step 1: Understanding the scenario
Imagine a box containing a total of 10 pens, of which:
- 6 pens have ink.
- 4 pens do not have ink.
These numbers are assumed based on a hypothetical situation to illustrate the solution, as the original question does not specify these details.
### Step 2: Probability of Event A
Event A: First pen has ink.
To find the probability of picking a pen with ink first, we take the number of pens with ink and divide it by the total number of pens:
[tex]\[
\text{Probability of Event A} = \frac{\text{Number of pens with ink}}{\text{Total number of pens}} = \frac{6}{10} = 0.6
\][/tex]
### Step 3: Probability of Event B given Event A
Event B: Second pen has no ink given the first had ink.
Once the first pen is selected and it's one with ink, the total number of pens decreases by one. Now there are 9 pens left in total.
The number of pens without ink remains the same (4 pens without ink), as the first pen selected in Event A was assumed to have ink.
Now, the probability of picking a pen with no ink on the second draw is:
[tex]\[
\text{Probability of Event B given Event A} = \frac{\text{Number of pens without ink}}{\text{Total pens remaining after first draw}} = \frac{4}{9} \approx 0.444
\][/tex]
### Step 4: Combined Probability of Events A and B
Now, to find the overall probability of both events happening (i.e., first selecting a pen with ink and then selecting a pen with no ink), multiply the probabilities of Event A and Event B given Event A:
[tex]\[
\text{Combined probability} = \text{Probability of Event A} \times \text{Probability of Event B given Event A} = 0.6 \times 0.444 \approx 0.267
\][/tex]
Thus, the probability that the first pen selected is one with ink and the second pen selected is one without ink is approximately 0.267.
1. Event A: The first selection is a pen with ink.
2. Event B: The second selection is a pen with no ink, given that the first was a pen with ink.
Let's break down the solution step by step:
### Step 1: Understanding the scenario
Imagine a box containing a total of 10 pens, of which:
- 6 pens have ink.
- 4 pens do not have ink.
These numbers are assumed based on a hypothetical situation to illustrate the solution, as the original question does not specify these details.
### Step 2: Probability of Event A
Event A: First pen has ink.
To find the probability of picking a pen with ink first, we take the number of pens with ink and divide it by the total number of pens:
[tex]\[
\text{Probability of Event A} = \frac{\text{Number of pens with ink}}{\text{Total number of pens}} = \frac{6}{10} = 0.6
\][/tex]
### Step 3: Probability of Event B given Event A
Event B: Second pen has no ink given the first had ink.
Once the first pen is selected and it's one with ink, the total number of pens decreases by one. Now there are 9 pens left in total.
The number of pens without ink remains the same (4 pens without ink), as the first pen selected in Event A was assumed to have ink.
Now, the probability of picking a pen with no ink on the second draw is:
[tex]\[
\text{Probability of Event B given Event A} = \frac{\text{Number of pens without ink}}{\text{Total pens remaining after first draw}} = \frac{4}{9} \approx 0.444
\][/tex]
### Step 4: Combined Probability of Events A and B
Now, to find the overall probability of both events happening (i.e., first selecting a pen with ink and then selecting a pen with no ink), multiply the probabilities of Event A and Event B given Event A:
[tex]\[
\text{Combined probability} = \text{Probability of Event A} \times \text{Probability of Event B given Event A} = 0.6 \times 0.444 \approx 0.267
\][/tex]
Thus, the probability that the first pen selected is one with ink and the second pen selected is one without ink is approximately 0.267.
Thank you for reading the article A box contains pens Some pens have ink and some do not A teacher randomly selects a pen and sets it aside Then another random. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Brahmana