Question

A lot of 20 bulbs contain 4 defective ones. One bulb is selected at random from the lot. What is the probability that this bulb is defective? Suppose the bulb selected in the previous case is not defective and is not replaced. Now one bulb is selected at random from the rest. What is the probability that this bulb is not defective?

Answer 1

Total no. of bulbs $=20$

No. of defective bulbs $=4$

Therefore,

$P\left(\text{getting a defective bulb}\right)=\frac{\text{No. of defective bulbs}}{\text{total no. of bulbs}}=\frac{4}{20}=\frac{1}{5}$

Now,

One non defective bulb is drawn then the total numbers of bulb left is $19$

Total numbers of bulbs $=19$

No. of defective bulbs $=4=4$

No. of non-defective bulbs $=19-4=15$

$P\left(\text{bulb is not defective}\right)=\frac{\text{No. of non-defective bulbs}}{\text{total numbers of bulbs}}=\frac{15}{19}$