PokerProblem.txt

# The Poker Test with Four Cards: 
# Suppose you have four cards which each take on values 0 to 9 independently and with replacement. 
# What is the probability of each of the following:
# 1. X cards are the same (i.e. 1 < X < = 4)
# 2. All cards are different (i.e. X = 1)
# 3. 2 pairs of cards that are the same, i.e. WWYY


# Code:
PT4 = function(n){ #n is the number of iterations
	unique = 0 #X = 1 (e.g. [3,4,6,7])
	one_pair = 0 #X = 2 (e.g. [3,3,9,7])
	one_tri = 0 #X = 3 (e.g. [3,3,3,7])
	two_pair = 0 #(e.g. [3,3,7,7])
	for (i in 1:n) {
		cards = sample(0:9,4,replace=T) #generate 4 cards with replacement
		result = table(cards)
		unique = unique + (length(result) == 4) #X = 1,the boolean value is 1 if true, 0 otherwise
		one_pair = one_pair + (length(result) == 3)
		one_tri = one_tri + (length(result) == 2 & max(result) == 3)
		two_pair = two_pair + (length(result) == 2 & max(result) == 2)
	}
	prob = cbind(unique,one_pair,one_tri,two_pair) / n #generate the probability table
	return(prob)
}

#Example:
n=5000

PT4(n)

#      unique one_pair one_tri two_pair
# [1,] 0.5202   0.4162   0.031   0.0312