Python中的相依概率

Question

我正在尝试用Python为自己制作一些东西，在我的例子中，这将决定在一副牌中绘制某张牌的可能性。牌组的大小由一个原始输入决定，也就是你试图计算出抽牌概率的牌的数量。现在，我有：

from __future__ import division

t = True
while True:
    if t == True:
        numCards = int(raw_input("How many cards in your deck? Type here: "))

        print "There are " + str(numCards) + " cards in your deck."

        whatCards = raw_input("What card are you testing for how likely it is to draw them? Type here: ")
        whatCards = whatCards.capitalize()
        print whatCards + " is a great card!"

        if whatCards.endswith("s"):
            numCards2 = int(raw_input("How many " + whatCards + " are in it? "))
            whatCards = whatCards + "s"
        elif whatCards.endswith("y"):
            numCards2 = int(raw_input("How many " + whatCards[:-1] + "ies are in it? "))
        else:
            numCards2 = int(raw_input("How many " + whatCards + "s are in it?"))

        if numCards2 > 1:
            print "Ok! There are " + str(numCards2) + " " + whatCards + "s" + "!"
        else:
            print "Alright. There is " + str(1) + " " + whatCards + "!"



        '''probability = (numCards2 / numCards) + (numCards2 / (numCards-1)) + (numCards2 / (numCards-2)) + \


(numCards2 / (numCards-3)) + (numCards2 / (numCards-4)) + (numCards2 / (numCards-5))\
                  + (numCards2 / (numCards-6))'''
    probability = numCards2 / numCards

    print "Results are approximate"
    print "Decimal: " + str(probability)

    if len(str(probability)) <= 3:
        print "Percentage: " + str(probability)[2] + str(0) + "%"
    else:
        print "Percentage: " + str(probability)[2] + str(probability)[3] + "%"

    print "Fraction: " + str(numCards2) + "/" + str(numCards)
    t = False

if t == False:
    numCards = int(raw_input("How many cards in your deck? Type here: "))

    print "There are " + str(numCards) + " cards in your deck."

    whatCards = raw_input("What card are you testing for how likely it is to draw them? Type here: ")
    whatCards = whatCards.capitalize()
    print whatCards + " is a great card!"

    if whatCards.endswith("s"):
        numCards2 = int(raw_input("How many " + whatCards + " are in it? "))
        whatCards = whatCards + "s"
    elif whatCards.endswith("y"):
        numCards2 = int(raw_input("How many " + whatCards[:-1] + "ies are in it? "))
    else:
        numCards2 = int(raw_input("How many " + whatCards + "s are in it?"))

    if numCards2 > 1:
        print "Ok! There are " + str(numCards2) + " " + whatCards + "s" + "!"
    else:
        print "Alright. There is " + str(1) + " " + whatCards + "!"



    '''probability = (numCards2 / numCards) + (numCards2 / (numCards-1)) + (numCards2 / (numCards-2)) + \
                  (numCards2 / (numCards-3)) + (numCards2 / (numCards-4)) + (numCards2 / (numCards-5))\
                  + (numCards2 / (numCards-6))'''
    probability = numCards2 / numCards

    print "Results are approximate"
    print "Decimal: " + str(probability)

    if len(str(probability)) <= 3:
        print "Percentage: " + str(probability)[2] + str(0) + "%"
    else:
        print "Percentage: " + str(probability)[2] + str(probability)[3] + "%"

    print "Fraction: " + str(numCards2) + "/" + str(numCards)
    t = True

正如你所看到的，它目前正在解决的是，只有一个平局的可能性。但是，我的目标是让用户输入他们自己的抽卡次数，比如说，他们有一个60张牌组，其中有15张沼泽牌，还有7张抽牌。问题是，如果我想画一手牌（7张），我不能让它计算出60张，然后59张，58张，再到53张的概率。这是因为，如果他们把沼泽地划出来，概率就会下降，从60降到53是不行的。我要做些什么来让它从y（牌组大小）中随机选择x张牌，并在“draw”时减少x的数量，并为每个“draw”更改y。而且它必须工作很多次，这取决于用户想要什么。谢谢！（希望这有意义…）

Answer 1

假设你有n张牌，你画了m张。可能的组合是n！/（n-m）！如果你在寻找绘制y张卡片（y<；=m）的概率，它占n张卡片总数的x。您必须考虑两个数量： 1从x张牌中选出y张牌的可能方法就是x！/（x-y）！然后可能的方法是把这个有序的集合放入m个插槽，或者把其他m-y卡放到m个卡的集合中，也就是m！/（m-y）！ 这两个量的乘积表示有利事件，而第一个数字表示事件总数。所以你的可能性是

p=x！m！（n-m）！/（n！（x-y）！（m-y）！）

我希望我没有错过任何东西：）