利用試算表模擬機率事件（2）

運用Excel軟體及內建函數來模擬機率事件，遠比親自實際體驗或執行撰寫程式更加簡便。作者在第15期蘭陽學報的文章中已介紹了一些使用方法及模擬程序，並以三個有名又有趣的問題當做範例，進行所有過程的操作與示範，不但可以輕鬆呈現正確的機率值，同時能夠親眼看到隨機的變化。只是該文僅觸及基本事件可以重複出現的狀況，對於抽籤、排隊順序、撲克牌洗牌等問題，則需要使用不同的函數加以組合及處理。我們依然會介紹幾個特別的問題，包含抽獎的順序是否會影響到得獎機率，這個疑問經常困擾著許多人，不過也有不少人應知其實是完全無關，我們利用數學計算及模擬呈現真實結果。另一個則是數學史上相當知名的錯排問題，簡單而言是指一群數字1,2,...,n任意排列，探究沒有任何一個數字在自己的位置上的個數或機率，生活中常會碰到類似案例，延伸的運用也很廣，只是這個問題推導及計算有些難度，但透過模擬卻能輕鬆設定及觀察，對於理解這個題目有相當大的助益。本文中將會介紹rank及index這兩個函數，一般而言，他們大多是用在資料的數據排序、參照回傳，我們搭配著亂數產生函數rand，就能順利模擬基本事件不得重複出現的機率問題。而這套方法除了可以處理機率事件之外，在生活中還會有許多特殊、有趣的用途，例如：座位安排、人員分組、中餐吃什麼？對於課堂、團體、職場而言，都能利用隨機性產生實質的幫助。其相關設定、操作方式及使用時機均會加以說明，相信大家都能輕鬆上手並靈活運用。

關鍵字

機率；試算表；錯排問題；排列組合；模擬

並列摘要

Using Excel software and built-in functions to simulate the probability events is much simpler than processing it through hand calculation or a customized computer program. For demonstration and examination, the author has taken three popular questions for examples to introduce the methods and the stimulation (see Lanyang Journal, 15th edition). It can be seen that the Excel not only generates the correct probability value with speed, but also it provides us an opportunity to closely observe the random changes. As the article has focused on the repetition of single events, questions with the draw, the queuing order, the poker shuffle, etc, will be processed through the combination of various functions and are to be discussed in this article. We will introduce two interesting questions, including whether the draw of the lottery will affect the chance of winning. Many people find this question puzzling whereas a number of people are aware that it is completely irrelevant. We present the actual situation by applying calculations and simulation. Another question we try to answer is the well-known derangement problem. In short, given a group of numbers 1,2,...,n, it explores the probability of not having each number stays in their own position. The derangement is quite common in real life situation, and it is widely applied to other fields. Although the derivation and calculation of derangement is more complicated, it can be easily processed and observed through stimulation. As a result, it provides us with a better understanding of this problem. We introduce two functions: Rank and Index. They are mostly used in sorting out the data and addressing to the reference. We use random numbers to generate function Rand, then we can successfully stimulate the probability of non-repetition of single events. Additionally, this method can be of great help and fun when dealing with life situations such as seat arrangement, group division, lunch decision, etc. As to the settings, the operation modes and the usage, we provide detail information which we believe can help everyone easily get started and make the best use.