Five bad oranges are accidentally mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence, find the mean and variance of the distribution.

Total oranges = 5+20 = 25

Let p = probability of drawing a bad orange

Let some bad oranges drawn be X.

X follows a binomial distribution with,

The required binomial distribution is given by,

So, mean = np

27