HMMT 二月 2017 · COMB 赛 · 第 1 题
HMMT February 2017 — COMB Round — Problem 1
题目详情
英文原题
- Kelvin the Frog is going to roll three fair ten-sided dice with faces labelled 0 , 1 , 2 , . . . , 9 . First he rollstwo dice, and finds the sum of the two rolls. Then he rolls the third die. What is the probability that the sum of the first two rolls equals the third roll?
解析
英文解析
- Kelvin the Frog is going to roll three fair ten-sided dice with faces labelled 0 , 1 , 2 , . . . , 9 . First he rollstwo dice, and finds the sum of the two rolls. Then he rolls the third die. What is the probability that the sum of the first two rolls equals the third roll?
Proposed by: Yang Liu
Answer:11
3200
First, there are 10 = 1000 triples ( a, b, c ) . Now, we should count how many of these triples satisfya + b = c. If c = 0, we get 1 triple (0 , 0 , 0). If c = 1, we get two triples (1 , 0 , 1) and (0 , 1 , 1) . Continuing,
this gives that the total number of triples is 1 + 2 + · · · + 10 = 55 . Therefore, our final answer is
55 11 = .
1000 200