Question

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

Answer 1

Hint- Make use of the formula of probability and find out the favourable outcomes in both the cases separately.

Complete step-by-step answer:

Given that the total number of pens=144=n(S)
Given that the total number of defective pens=20=n(E)
The total number of non defective pens=$n(\mathop E\limits^ - )$ =144-20=124
Given that Nuri will buy a pen only if it is detective
So, let us solve the first part, that is the probability that she will buy it
(i)She will buy a pen only if it is defective
So, the number of defective pens=no of favourable outcomes=n(E)=20
Total number of pens=Total no of outcomes=n(S)=144
So, the probability=$\dfrac{{No{\text{ of favourable outcomes}}}}{{Total{\text{ no of possible outcomes}}}} = \dfrac{{n(E)}}{{n(S)}} = \dfrac{{20}}{{144}} = \dfrac{5}{{36}}$ =P(B)
So, the probability that she will buy a pen=$\dfrac{5}{{36}}$
(ii)Now, let us find out the second part, that is the probability that she will not buy a pen
She will not buy a pen a pen if it is non defective
So, the probability would be , the total probability –the probability if she would buy a pen
The only two events which are possible are NURI buying a pen or not buying a pen,
Since both of them are complements of each other , the sum of these two events will be 1
So, we can write P(B)+ $P(\mathop B\limits^ - )$=1
We have to find out the probability that she will not buy a pen
 $P(\mathop B\limits^ - )$=1-P(B)
$P(\mathop B\limits^ - )$=1-$\dfrac{5}{{36}}$
$P(\mathop B\limits^ - )$=$\dfrac{{36 - 5}}{{36}} = \dfrac{{31}}{{36}}$
So, the probability that she would not buy a pen = $\dfrac{{31}}{{36}}$

Note: When solving these types of problems, first always try to find out the total number of outcomes and from that find out the favourable outcomes in each of the cases separately.