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HMMT 二月 2014 · 冲刺赛 · 第 5 题

HMMT February 2014 — Guts Round — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 5 ] If four fair six-sided dice are rolled, what is the probability that the lowest number appearing onany die is exactly 3?
    n + 83
解析

英文解析

  1. [ 5 ] If four fair six-sided dice are rolled, what is the probability that the lowest number appearing onany die is exactly 3?
    Answer: 175/1296 The probability that all the die rolls are at least 3 is . The probability 44
    they are all at least 4 is . The probability of being in the former category but not the latter is thus 346
    4 46
    4 3 256 − 81 175 − = = .
    6 6 1296 1296
    n + 83