A combination lock has numbers from 0 to 30 and takes a three-number combination to open it. If you try all the combinations that have the identical numbers, like 12-12-12 or 7-7-7, what is the probability you will open the lock?

There are 31 possible combinations where all three numbers are identical(e.g. 0-0-0, 1-1-1, 2-2-2,.......,30-30-30).

Total combinations possible for the lock when numbers are from 0 to 30 = 31*31*31

Hence, the probability of opening the lock by trying all the combinations with identical numbers is

=> possible outcomes / total number of outcomes = $$\dfrac{31}{31\times\ 31\times\ 31}$$ = $$\dfrac{1}{31\times\ 31}$$

=> $$\dfrac{1}{961}$$ 

The answer is option A.