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]
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
