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HMMT 十一月 2008 · 冲刺赛 · 第 6 题

HMMT November 2008 — Guts Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] Sarah is deciding whether to visit Russia or Washington, DC for the holidays. She makes herdecision by rolling a regular 6-sided die. If she gets a 1 or 2, she goes to DC. If she rolls a 3 , 4 , or 5,
    she goes to Russia. If she rolls a 6, she rolls again. What is the probability that she goes to DC?
    1 HARVARD-MIT NOVEMBER TOURNAMENT, 8 NOVEMBER 2008 — GUTS ROUNDst
    2 2
解析

英文解析

  1. [ 6 ] Sarah is deciding whether to visit Russia or Washington, DC for the holidays. She makes herdecision by rolling a regular 6-sided die. If she gets a 1 or 2, she goes to DC. If she rolls a 3 , 4 , or 5,
    she goes to Russia. If she rolls a 6, she rolls again. What is the probability that she goes to DC?
    Answer: On each roll, the probability that Sarah decides to go to Russia is 3 / 2 times the 2
    probability she decides to go to DC. So, the total probability that she goes to Russia is 3 / 2 times 5
    the total probability that she goes to DC. Since these probabilities sum to 1 (they are the only two
    2 3
    eventual outcomes) Sarah goes to DC with probability and Russia with probability .
    5 5
    st 1
    1 HARVARD-MIT NOVEMBER TOURNAMENT, 8 SATURDAY 2008 — GUTS ROUND
    2 2