Question 917032
All factors of 10^99 are of the form *[tex \large 2^a 5^b] where *[tex \large 0 \le a,b \le 99].


For the factor to be a multiple of 10^88, we must have *[tex \large a \ge 88] and *[tex \large b \ge 88]. We have 12 choices (88, 89, ..., 99) for a and 12 choices for b, so 144 choices total. There are 100^2 factors of 10^99, so the probability is 144/10000.