Random digits are integers selected from among 0,1,2,3,4,5,6,7,8,9 one at a time in such a way that at each stage in the selection process the integer chosen is just as likely to be one digit as any other. In simulation experiments it is often necessary to generate a series of random digits. This can be done in a number of ways, the most common being by means of a computerized random number generator. In generating such a series, consider the number of trials needed to obtain the first zero.

(a) What’s the probability that exactly three trials are needed?

(b) What’s the probability that no more than three trials are needed?

(c) What’s the probability that no less than a hundred trials are needed?

(d) What’s the expected number of trials needed to obtain the first zero?