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HMMT 十一月 2013 · GEN 赛 · 第 4 题

HMMT November 2013 — GEN Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 4 ] A 50-card deck consists of 4 cards labeled “ i ” for i = 1 , 2 , . . . , 12 and 2 cards labeled “13”. If Bobrandomly chooses 2 cards from the deck without replacement, what is the probability that his 2 cardshave the same label?
解析

英文解析

  1. [ 4 ] A 50-card deck consists of 4 cards labeled “ i ” for i = 1 , 2 , . . . , 12 and 2 cards labeled “13”. If Bobrandomly chooses 2 cards from the deck without replacement, what is the probability that his 2 cardshave the same label?
    Answer: All pairs of distinct cards (where we distinguish cards even with the same label) are 73
    1225
    ( ) ( ) ( )
    2 4 50
    equally likely. There are + 12 = 73 pairs of cards with the same label and = 100 · = 122549
    2 2 2 4
    pairs of cards overall, so the desired probability is .73
    1225