Welcome to the article A junk drawer at home contains five pens two 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 :
The probability that you randomly grab two pens from the drawer and don’t end up with a pen that works is [tex]\dfrac{4}{25}[/tex].
Given information:
The number of pens in the drawer is [tex]n=5[/tex].
The number of pens that doesn't work is [tex]a=2[/tex].
So, the number of pens which works will be, [tex]b=5-2=3[/tex].
The probability of grabbing a pen that doesn't work will be,
[tex]P_a=\dfrac{2}{5}[/tex]
Now, two pens are grabbed randomly from the drawer. So, the probability that you randomly grab two pens from the drawer and don’t end up with a pen that works will be calculated as,
[tex]P=(P_a)^2\\P=\dfrac{2}{5}\times \dfrac{2}{5}\\P=\dfrac{4}{5}[/tex]
Therefore, the value of the required probability will be [tex]\dfrac{4}{5}[/tex].
To know more about the random picking, refer to the link:
https://brainly.com/question/13448455
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Rewritten by : Brahmana
Answer:
The probability is [tex]P(k) = \frac{4}{25}[/tex]
Step-by-step explanation:
From the question we are told that
The number of pens from the drawer is n = 5
The number of pens that doesn't work is k = 2
The probability that a does not work is
[tex]p = \frac{k}{n}[/tex]
=> [tex]p = \frac{2}{5}[/tex]
The probability that a pen works is
[tex]q = 1- p[/tex]
[tex]q = 1- \frac{2}{5}[/tex]
=> [tex]q = \frac{3}{5}[/tex]
Generally the probability that ending up with a pen that doesn't work is mathematically represented as
[tex]P(k) = p^2[/tex]
=> [tex]P(k) = [\frac{2}{5} ]^2[/tex]
=> [tex]P(k) = \frac{4}{25}[/tex]