HMMT 二月 2001 · 冲刺赛 · 第 6 题

HMMT February 2001 — Guts Round — Problem 6

[8] Six students taking a test sit in a row of seats with aisles only on the two sides of the row. If they finish the test at random times, what is the probability that some student will have to pass by another student to get to an aisle?

解析

[8] Six students taking a test sit in a row of seats with aisles only on the two sides of the row. If they finish the test at random times, what is the probability that some student will have to pass by another student to get to an aisle? 1 Solution: The probability p that no student will have to pass by another student to get to an aisle is the probability that the first student to leave is one of the students on the end, 2 2 2 2 the next student to leave is on one of the ends of the remaining students, etc.: p = · · · , 6 5 4 3 43 so the desired probability is 1 − p = . 45