Question

A lot consists of $144$ ball pens of which $20$ are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. 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

The total numbers of outcomes i.e. pens $=144$

Given, numbers of defective pens $=20$

$\therefore$ The numbers of non defective pens $=144-20=124$

$P\left(E\right)=\frac{Numberoffavourableoutcomes}{Totalnumberofoutcomes}$

Step $\mathbf{1}$: Find the probability that she will buy the pens.

Total numbers events in which she will buy them $=124$

So,

$$\begin{gathered} P\left(buying\right)=\frac{124}{144} \\ =\frac{31}{36} \\ =\mathbf{0}\mathbf{.}\mathbf{86} \end{gathered}$$

Hence, the probability that she will buy the pens is $\mathbf{0}\mathbf{.}\mathbf{86}$.

Step $\mathbf{2}$: Find the probability that she will not buy the pens.

Total numbers of events in which she will not buy them $=20$

So,

$$\begin{gathered} P\left(buying\right)=\frac{20}{144} \\ =\frac{5}{36} \\ =\mathbf{0}\mathbf{.}\mathbf{138} \end{gathered}$$

Hence, the probability that she will not buy the pens is $\mathbf{0}\mathbf{.}\mathbf{138}$.