Welcome to the article A junk drawer at home contains six pens three of which work What is the probability that you randomly grab two pens from the drawer. 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 find the probability of randomly grabbing two pens from the drawer and ending up with none that work, we need to first determine the number of non-working pens and the total number of pens.
1. Identify the Total and Non-working Pens:
- Total pens in the drawer: 6
- Working pens: 3
- Therefore, non-working pens [tex]\(= 6 - 3 = 3\)[/tex]
2. Calculate the Probability of Selecting Non-working Pens:
- When randomly selecting two pens, we want both to be non-working. We calculate this probability in two steps:
- For the first pick: The probability of choosing a non-working pen out of the total pens is [tex]\(\frac{3}{6}\)[/tex].
- After picking one non-working pen, there are now 5 pens left in total and 2 non-working pens remaining. So, for the second pick: The probability is [tex]\(\frac{2}{5}\)[/tex].
3. Calculate the Combined Probability:
- Multiply the probabilities of both selections since we want both events to occur:
[tex]\[
\left(\frac{3}{6}\right) \times \left(\frac{2}{5}\right) = \frac{3}{15} = \frac{1}{5} = 0.2
\][/tex]
Therefore, the probability of selecting two pens and having both be non-working is [tex]\(0.2\)[/tex].
1. Identify the Total and Non-working Pens:
- Total pens in the drawer: 6
- Working pens: 3
- Therefore, non-working pens [tex]\(= 6 - 3 = 3\)[/tex]
2. Calculate the Probability of Selecting Non-working Pens:
- When randomly selecting two pens, we want both to be non-working. We calculate this probability in two steps:
- For the first pick: The probability of choosing a non-working pen out of the total pens is [tex]\(\frac{3}{6}\)[/tex].
- After picking one non-working pen, there are now 5 pens left in total and 2 non-working pens remaining. So, for the second pick: The probability is [tex]\(\frac{2}{5}\)[/tex].
3. Calculate the Combined Probability:
- Multiply the probabilities of both selections since we want both events to occur:
[tex]\[
\left(\frac{3}{6}\right) \times \left(\frac{2}{5}\right) = \frac{3}{15} = \frac{1}{5} = 0.2
\][/tex]
Therefore, the probability of selecting two pens and having both be non-working is [tex]\(0.2\)[/tex].
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Rewritten by : Brahmana