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?

Use the theoretical definition of probability

1. The number of all possible outcomes is , because the first number can be selected from 8 numbers from the set {0, 1, 2, 3, 4, 5 ,6 ,7}, the second number can be selected from all 8 numbers from this set and the third number can be also selected from all  8 numbers from this set.

2. The number of favorable outcomes is 8. All favorable outcomes are:

3. The probability that the player will win a prize is

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.