HMMT 十一月 2019 · 冲刺赛 · 第 2 题

HMMT November 2019 — Guts Round — Problem 2

[5] You are trying to cross a 6 foot wide river. You can jump at most 4 feet, but you have one stone you can throw into the river; after it is placed, you may jump to that stone and, if possible, from there to the other side of the river. However, you are not very accurate and the stone ends up landing uniformly at random in the river. What is the probability that you can get across?

解析

[5] You are trying to cross a 6 foot wide river. You can jump at most 4 feet, but you have one stone you can throw into the river; after it is placed, you may jump to that stone and, if possible, from there to the other side of the river. However, you are not very accurate and the stone ends up landing uniformly at random in the river. What is the probability that you can get across? Proposed by: Carl Schildkraut and Milan Haiman 1 Answer: 3 To be able to cross, the stone must land between 2 and 4 feet from the river bank you are standing 2 1 on. Therefore the probability is = . 6 3