Question

A lot consists of $ 144 $ ball pens of which $ 20 $ are defective and the other are good. Nuri will buy a pen if it is good, but will not buy it if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that. She will buy it?

Answer 1

Hint: To find required probability we first find number of good ball pens in a lot finding the difference of total number of pens and number of defective pens in a lot and then find ratio of number of good pens to total numbers of pens in a lot to get required probability or required solution of given problem.

Complete step-by-step answer:
Total numbers of ball pens = $ 144 $
Number of defective ball pens = $ 20 $
Therefore, the number of ball pens which are not defective or working good can be find by calculating the difference of total pens and number of defective pens.
Hence, number of good ball pens = $ 144 - 20 $
= $ 124 $
Hence, we see that a lot consists of $ 144 $ ball pens out of which $ 20 $ are defective and $ 124 $ are good ball pens.
Since, it is given that Nuri will buy a pen if it is good, but will not buy if it is defective.
Therefore, to find required probability or probability that Nuri will buy a pen will be given as:
 $ \dfrac{{Number\,\,of\,good\,\,ball\,\,pens\,\,in\,\,a\,\,lot}}{{Total\,\,number\,\,of\,\,pens\,\,in\,\,a\,\,lot}} $
Substituting values in above. We have,
Probability that Nuri will buy a pen = $ \dfrac{{124}}{{144}} $
 $ = \dfrac{{31}}{{36}} $
Hence, from above we see that the probability that Nuri will buy a ball pen from a lot of $ 144 $ ball pens is $ \dfrac{{31}}{{36}} $ .
So, the correct answer is “ $ \dfrac{{31}}{{36}} $ ”.

Note: We can also find the solution of a given problem in another way. In this way we first calculate the probability of defective pen from a given lot of pens and then subtracting the value obtained from one to get the required probability of a good pen or we can say required solution of the given problem.