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Question

所以我正在研究统计问题，问题是 "Six kids are standing in line. What is the probability that they are in alphabetical order by name? Assume no two children have the same exact name." 我在 R 中使用 sample() 和 rle() 函数，但我对如何计算概率感到困惑.我可以得到一些帮助吗？

这也是我目前的代码：

kids <- sample(c("A", "B", "C", "D", "E", "F"), 6, replace = TRUE)
table(kids)
head(kids)
rle(c("A", "B", "C", "D", "E", "F"))
kids.rle <- rle(kids)
str(kids.rle)
sort(kids.rle$lengths, decreasing = TRUE)

Answer 1

如@YOLO 所述，理论概率为 1 / 720，可以在 R 中计算为 1 / factorial(6)。但是，您也可以轻松地在脑海中计算出来。如果您想运行一个小的模拟来表明随着重复次数的增加，观察到的概率收敛到理论概率，计算能力会派上用场：

kids_ordered <- c("A", "B", "C", "D", "E", "F")

n <- 1000000 # number of repetition
result <- rep(NA, n) # vector to hold outcomes

set.seed(147) # seed for reproducibility

# reorder kids n times and check if the outcome is in alphabetical order each time
for(i in seq_len(n)) {
  result[i] <- all(sample(kids) == kids_ordered)
}

# compute the probability
mean(result)
# [1] 0.001376

结果非常接近1 / 720 = 0.001389

站成一排的学生

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