HMMT 二月 2014 · 冲刺赛 · 第 5 题
HMMT February 2014 — Guts Round — Problem 5
题目详情
- [ 5 ] If four fair six-sided dice are rolled, what is the probability that the lowest number appearing on any die is exactly 3? 3 n + 8
解析
- [ 5 ] If four fair six-sided dice are rolled, what is the probability that the lowest number appearing on any die is exactly 3? 4 4 Answer: 175/1296 The probability that all the die rolls are at least 3 is . The probability 6 4 3 they are all at least 4 is . The probability of being in the former category but not the latter is thus 6 4 4 4 3 256 − 81 175 − = = . 6 6 1296 1296 3 n + 8