HMMT 十一月 2017 · 冲刺赛 · 第 17 题

HMMT November 2017 — Guts Round — Problem 17

[ 7 ] A standard deck of 54 playing cards (with four cards of each of thirteen ranks, as well as two Jokers) is shuffled randomly. Cards are drawn one at a time until the first queen is reached. What is the probability that the next card is also a queen?

解析

[ 7 ] A standard deck of 54 playing cards (with four cards of each of thirteen ranks, as well as two Jokers) is shuffled randomly. Cards are drawn one at a time until the first queen is reached. What is the probability that the next card is also a queen? Proposed by: Serina Hu 2 Answer: 27 Since the four queens are equivalent, we can compute the probability that a specific queen, say the queen of hearts, is right after the first queen. Remove the queen of hearts; then for every ordering of the 53 other cards, there are 54 locations for the queen of hearts, and exactly one of those is after the first queen. Therefore the probability that the queen of hearts immediately follows the first queen is 1 1 2 , and the probability any queen follows the first queen is · 4 = . 54 54 27