HMMT 二月 2007 · COMB 赛 · 第 3 题
HMMT February 2007 — COMB Round — Problem 3
题目详情
英文原题
- [ 4 ] Jack, Jill, and John play a game in which each randomly picks and then replaces a card from astandard 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
英文解析
- [ 4 ] Jack, Jill, and John play a game in which each randomly picks and then replaces a card from astandard 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.)
Answer: . The desired probability is the relative probability that Jill draws the spade. In the first 12
round, Jack, Jill, and John draw a spade with probability 1 / 4 , 3 / 4 · 1 / 4, and (3 / 4) · 1 / 4 respectively.237
Thus, the probability that Jill draws the spade is
3 / 4 · 1 / 4 12 = .
1 / 4 + 3 / 4 · 1 / 4 + (3 / 4) · 1 / 4 372