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

We have,

No. of good pens $=144–20=124$

No. of detective pens $=20$

Therefore, Total no. of possible outcomes $=144$ (total no. of pens)

(i) So, for her to buy it the pen should be a good one.

So, let E be the event of buying a pen which is good.

Therefore No. of favorable outcomes $=124$ ($124$ good pens)

As we know Probability, P(E) = Number of favorable outcomes/ Total number of outcomes

P(E) $=124/144=31/36$

(ii)  Now, let

$(\overset{\scriptscriptstyle\rightharpoonup}{E})$be the Event of she not buying a pen as it was a defective one.

$P(\overset{\scriptscriptstyle\rightharpoonup}{E})+P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1$

$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1-P(E)$

$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1-\frac{31}{36}$

$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=\frac{56}{36}$

Thus, the probability that she will not buy $=5/36$