The <em><u>correct answer</u></em> is:
0.3439.
Explanation:
This is a binomial probability. This is because there are two outcomes; either a digit is 0 or it is not. Since the digits are used with replacement, the probability of one digit being a 0 does not affect the probability of a second digit being 0. Finally, there are a fixed number of trials; we are choosing 4 digits.
Since we want the probability that <em>at least</em> one digit is a zero, we want the complement of "no digits are zero". This means we will find P(X = 0) and subtract it from 1.
The formula for a binomial distribution with n trials and r successes is
In this situation, n is 4, since we are choosing 4 digits. r is 0, since we are finding the probability that no digits are 0. p is 0.1, since there is a 1/10 chance of a digit being 0. This gives us:
This means that the complement of P(X=0), or the probability that at least one digit is 0, is 1-0.6561 = 0.3439.