Question

A box contains $144$ pens of which $20$ are defective and the others are good. A person will buy a pen if it is good and will not buy if it is defective. The shopkeeper draws one pen from the box at random and gives it to the person. What is the probability that the person will buy it.

Answer 1

It is given that a box contains $144$ pens of which $20$ are defective. Therefore, the number of possible outcomes are $144$.

Now, if a person buy a pen and shopkeeper draws one pen at random from the total number of pens, then the possible outcome of getting a good pen is $144-20=124$, which means the number of favourable outcome is $124$.

Therefore, probability $P$ of person buying a pen or the probability of buying a non-defective pen is:

$P=\frac{124}{144}=\frac{31}{36}$

Hence, the probability of person buying a pen is $\frac{31}{36}$.