If there are n integers, the total outcomes are n * n = n^2.
If the integers are from x to y inclusive, and there are n = y - x + 1 integers.
For Ann's number to be greater than Bob's:
- If Bob selects the smallest number (x), Ann can select any of the n - 1 larger numbers.
- If Bob selects the next number (x + 1), Ann can select any of the n - 2 larger numbers.
...
- If Bob selects the largest number (y), Ann cannot select a larger number (0 possibilities).
So total favorable outcomes = (n - 1) + (n - 2) + ... + 1 + 0 = n(n - 1)/2
The probability P(Ann > Bob) = [n(n - 1)/2] / n^2 = (n - 1)/2n.
(1) y - x = 9
The number of integers is n = y - x + 1 = 10.
P(Ann > Bob) = (10 - 1)/(2*10) = 9/20.
Statement (1) alone is sufficient.
(2) y = -20
This tells us y is -20, but we don't know x, so we don't know the range. Without knowing x, we can't determine n, and thus can't find the probability.
Statement (2) alone is insufficient.
Answer A