Computing the probability of drawing two identical numbers out of a hat

permutations of samples.R

# Computing the probability of drawing two identical
# numbers out of a hat



# Incorrect - binomial distribution ---------------------------------------

# Use pbinom() to compute a probability curve for binomial 
# distribution

x <- pbinom(q = 0:10, size = 10, prob = 0.1)
plot(0:10, 1-x, type="b", lwd=2,
     main="Incorrect analysis - binomial distribution",
     xlab=NA,
     ylab="Probability")


# Computing all permutations ----------------------------------------------

# Use a function inside permn() to reduce memory consumption. Rather 
# than returning the entire permutation in each step, return the 
# count of positional matches

library(combinat)
y <- permn(1:10, function(x)sum(x == 1:10))
z <- table(unlist(y))
plot(z/sum(z), type="b",
     main="Permutation analysis",
     xlab=NA,
     ylab="Probability")


# Simulating the draws ----------------------------------------------------

n <- 1e6
z <- replicate(n, sum(sample.int(10) == 1:10))
plot(table(z)/n, type="b",
     main="Using simulation rather than permutation",
     xlab=NA,
     ylab="Probability")