As a part of a contest, a computer picks a digit from 0 to 7, inclusive, 3 times. if the 3 digits are all the same, the contestant wins a prize. what is the probability that the player will win a prize?

There are 8 numbers for the computer to choose from.
So the probability of choosing a particular number is 1/8.
The first number can be any one of the 8.
The second and the third must be the same as the first, with probability 1/8.

Therefore the probability that all three numbers are the same
= (1/8)(1/8) = 1/64   [ player will win a prize ] 
(=0.03125)