HMMT 二月 2003 · GEN2 赛 · 第 8 题
HMMT February 2003 — GEN2 Round — Problem 8
题目详情
- If x ≥ 0, y ≥ 0 are integers, randomly chosen with the constraint x + y ≤ 10, what is the probability that x + y is even?
解析
- If x ≥ 0, y ≥ 0 are integers, randomly chosen with the constraint x + y ≤ 10, what is the probability that x + y is even? Solution: 6 / 11 For each p ≤ 10, if x + y = p , x can range from 0 to p , yielding p + 1 ordered pairs ( x, y ). Thus there are a total of 1 + 2 + 3 + · · · + 11 allowable ordered pairs ( x, y ), but 1 + 3 + 5 + · · · + 11 of these pairs have an even sum. So the desired probability is 2 1 + 3 + 5 + · · · + 11 6 6 = = . 1 + 2 + 3 + · · · + 11 11 · 6 11