#Cards and Beans

#Simulations of the experiments described in Lecture 2.

from pylab import *

#Cards.  We model the deck as the list of integers
#0 to 51, so the rank of card i is 1 + i//4 and the suit
#is i%4

#Pull two cards from the deck and estimate the probability
#that they have the same rank.  There are options for the
#number of trials and whether this is done with or without
#replacement. Default is with replacement.

def card_sim(numtrials, repl=True):
    count=0
    for j in range(numtrials):
        sample=choice(arange(52),2,replace=repl)
        if sample[0]//4==sample[1]//4:
            count+=1
    return count/numtrials

#A bin contains b beans of each of three colors (0,1,2).
#Pull out 3 beans (with or without replacement).  What is
#the probability that all three are different?

def bean_sim(b,numtrials,repl=True):
    beans=[0]*b+[1]*b+[2]*b #the jar
    count=0
    for j in range(numtrials):
        sample=choice(beans,3,replace=repl)
        if (0 in sample) and (1 in sample) and (2 in sample):
            count+=1
    return count/numtrials

#Return a random permutation of the integers 1,...,n
def random_perm(n):
    return choice(arange(1,n+1),n,replace=False)