A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same is

Three-digit numbers are 100, 101, ..., 999. Total number of such numbers is 900.. The three-digit numbers (which have all same digits) are 111, 222, 333, ..., 999. Favorable number of cases is 9. Therefore, the required probability is9900=1100