A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

Let us assume that number of balls with digit marked as zero among the experiment of 4 balls drawn simultaneously be x.

As we can see that the balls are drawn with replacement, thus, the trial is a Bernoulli trial.

Probability of a ball drawn from the bag to be marked as digit

It can be clearly observed that X has a binomial distribution with

Thus, P(X = x) = nCxqn-xpx , where x = 0, 1, 2, …n

Probability of no ball marked with zero among the 4 balls = P(X = 0)