To find the probability that an integer randomly selected from the set {1, 2, 3, ..., 25} is an integer multiple of 2 or 5 but not both, we need to calculate the number of integers in the set that satisfy this condition and divide it by the total number of integers in the set.
First, let's count the integers that are multiples of 2 or 5. For multiples of 2, we have: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. That's a total of 12 integers.
For multiples of 5, we have: 5, 10, 15, 20, 25. That's a total of 5 integers.
Now, we need to find the integers that are multiples of 2 or 5 but not both. These are the integers that belong to either the multiples of 2 group or the multiples of 5 group, but not both.
The integers that are multiples of 2 but not multiples of 5 are: 2, 4, 6, 8, 12, 14, 16, 18, 22, 24. That's a total of 10 integers.
The integers that are multiples of 5 but not multiples of 2 are: 5, 15, 25. That's a total of 3 integers.
To find the integers that are multiples of 2 or 5 but not both, we add the counts of these two groups: 10 + 3 = 13 integers.
The total number of integers in the set {1, 2, 3, ..., 25} is 25.
Therefore, the probability that an integer randomly selected from the set is an integer multiple of 2 or 5 but not both is 13/25.