HMMT 二月 2007 · COMB 赛 · 第 3 题

HMMT February 2007 — COMB Round — Problem 3

[ 4 ] Jack, Jill, and John play a game in which each randomly picks and then replaces a card from a standard 52 card deck, until a spades card is drawn. What is the probability that Jill draws the spade? (Jack, Jill, and John draw in that order, and the game repeats if no spade is drawn.)

解析

[ 4 ] Jack, Jill, and John play a game in which each randomly picks and then replaces a card from a standard 52 card deck, until a spades card is drawn. What is the probability that Jill draws the spade? (Jack, Jill, and John draw in that order, and the game repeats if no spade is drawn.) 12 Answer: . The desired probability is the relative probability that Jill draws the spade. In the first 37 2 round, Jack, Jill, and John draw a spade with probability 1 / 4 , 3 / 4 · 1 / 4, and (3 / 4) · 1 / 4 respectively. Thus, the probability that Jill draws the spade is 3 / 4 · 1 / 4 12 = . 2 1 / 4 + 3 / 4 · 1 / 4 + (3 / 4) · 1 / 4 37