The digits after the decimal point of a random number betwee

The digits after the decimal point of a random number between 0 and 1 are numbers selected at random, with replacement, independently, and successively from the set {0,1,..., 9}.

In a random number from (0,1), on the average, how many digits are there before the number [3] occurs [9] times?

Solution

As the probability of each digit is 1/10, the expected number of trials until 9 3\'s is simply 9/(1/10) = 90