From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of a number of defective bulbs. Hence, find the mean of the distribution.

Out of 15 bulbs, five are defective.

Let p = probability that drawn bulb is defective

Also, the q = probability that drawn bulb is not defective.

Let X be the probability that the drawn bulb is defective out of 4.

Then, X follows a binomial distribution with,

The required binomial distribution is given by,

Let, X, be the random variable getting defective ball, so,