HMMT 二月 2003 · GEN2 赛 · 第 8 题
HMMT February 2003 — GEN2 Round — Problem 8
题目详情
英文原题
- If x ≥ 0, y ≥ 0 are integers, randomly chosen with the constraint x + y ≤ 10, what isthe probability that x + y is even?
解析
英文解析
- If x ≥ 0, y ≥ 0 are integers, randomly chosen with the constraint x + y ≤ 10, what isthe 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
1 + 3 + 5 + · · · + 11 6 62 = = .
1 + 2 + 3 + · · · + 11 11 · 6 11