확률계산 및 시뮬레이션

확률계산(같은 것이 있는 순열).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 확률 계산"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q: 주머니 속에 숫자 1이 적힌 카드가 세 장, 숫자 2가 적힌 카드가 3장, 3이 적힌 카드가 3장이 들어있다. \n",
    "이 주머니에서 임의로 세장의 카드를 동시에 뽑을 때, 카드에 적힌 숫자의 합이 3의 배수가 될 확률은?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.35714285714285715"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5/14 #답"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 시뮬레이션"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "card=[1,1,1,2,2,2,3,3,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "random.shuffle(card)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 3, 1, 2, 3, 1, 1, 2, 2]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "card"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 3, 1]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "card[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "count=100000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sus=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "성공확률은 0.35674이다\n"
     ]
    }
   ],
   "source": [
    "for i in range(count):\n",
    "    random.shuffle(card)\n",
    "    if sum(card[:3]) % 3 ==0:\n",
    "        sus=sus+1\n",
    "print(\"성공확률은 {}이다\".format(sus/count))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 전수조사"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "carddic={'a1':1,'a2':1,'a3':1,'b1':2,'b2':2,'b3':2,'c1':3,'c2':3,'c3':3}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['a1', 'a2', 'a3', 'b1', 'b2', 'b3', 'c1', 'c2', 'c3'])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carddic.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_values([1, 1, 1, 2, 2, 2, 3, 3, 3])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carddic.values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_items([('a1', 1), ('a2', 1), ('a3', 1), ('b1', 2), ('b2', 2), ('b3', 2), ('c1', 3), ('c2', 3), ('c3', 3)])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "carddic.items()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<itertools.permutations at 0x110098ca8>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "itertools.permutations(carddic.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "362880"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(list(itertools.permutations(carddic.keys())))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "362880"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "9*8*7*6*5*4*3*2*1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "per_with_eq=itertools.permutations(carddic.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "a=set((per_with_eq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1680"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1680은 같은 것이 있는 순열의 수임."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "504"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(list(itertools.permutations(carddic.keys(),3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "504"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "9*8*7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "84"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(list(itertools.combinations(carddic.keys(),3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 84는 9C3 의 개수임 , 즉 위의 list가 근원사건의 집합이라고 볼 수 있음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "standard=list(itertools.combinations(carddic.keys(),3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('a1', 'a2', 'a3'),\n",
       " ('a1', 'a2', 'b1'),\n",
       " ('a1', 'a2', 'b2'),\n",
       " ('a1', 'a2', 'b3'),\n",
       " ('a1', 'a2', 'c1'),\n",
       " ('a1', 'a2', 'c2'),\n",
       " ('a1', 'a2', 'c3'),\n",
       " ('a1', 'a3', 'b1'),\n",
       " ('a1', 'a3', 'b2'),\n",
       " ('a1', 'a3', 'b3'),\n",
       " ('a1', 'a3', 'c1'),\n",
       " ('a1', 'a3', 'c2'),\n",
       " ('a1', 'a3', 'c3'),\n",
       " ('a1', 'b1', 'b2'),\n",
       " ('a1', 'b1', 'b3'),\n",
       " ('a1', 'b1', 'c1'),\n",
       " ('a1', 'b1', 'c2'),\n",
       " ('a1', 'b1', 'c3'),\n",
       " ('a1', 'b2', 'b3'),\n",
       " ('a1', 'b2', 'c1'),\n",
       " ('a1', 'b2', 'c2'),\n",
       " ('a1', 'b2', 'c3'),\n",
       " ('a1', 'b3', 'c1'),\n",
       " ('a1', 'b3', 'c2'),\n",
       " ('a1', 'b3', 'c3'),\n",
       " ('a1', 'c1', 'c2'),\n",
       " ('a1', 'c1', 'c3'),\n",
       " ('a1', 'c2', 'c3'),\n",
       " ('a2', 'a3', 'b1'),\n",
       " ('a2', 'a3', 'b2'),\n",
       " ('a2', 'a3', 'b3'),\n",
       " ('a2', 'a3', 'c1'),\n",
       " ('a2', 'a3', 'c2'),\n",
       " ('a2', 'a3', 'c3'),\n",
       " ('a2', 'b1', 'b2'),\n",
       " ('a2', 'b1', 'b3'),\n",
       " ('a2', 'b1', 'c1'),\n",
       " ('a2', 'b1', 'c2'),\n",
       " ('a2', 'b1', 'c3'),\n",
       " ('a2', 'b2', 'b3'),\n",
       " ('a2', 'b2', 'c1'),\n",
       " ('a2', 'b2', 'c2'),\n",
       " ('a2', 'b2', 'c3'),\n",
       " ('a2', 'b3', 'c1'),\n",
       " ('a2', 'b3', 'c2'),\n",
       " ('a2', 'b3', 'c3'),\n",
       " ('a2', 'c1', 'c2'),\n",
       " ('a2', 'c1', 'c3'),\n",
       " ('a2', 'c2', 'c3'),\n",
       " ('a3', 'b1', 'b2'),\n",
       " ('a3', 'b1', 'b3'),\n",
       " ('a3', 'b1', 'c1'),\n",
       " ('a3', 'b1', 'c2'),\n",
       " ('a3', 'b1', 'c3'),\n",
       " ('a3', 'b2', 'b3'),\n",
       " ('a3', 'b2', 'c1'),\n",
       " ('a3', 'b2', 'c2'),\n",
       " ('a3', 'b2', 'c3'),\n",
       " ('a3', 'b3', 'c1'),\n",
       " ('a3', 'b3', 'c2'),\n",
       " ('a3', 'b3', 'c3'),\n",
       " ('a3', 'c1', 'c2'),\n",
       " ('a3', 'c1', 'c3'),\n",
       " ('a3', 'c2', 'c3'),\n",
       " ('b1', 'b2', 'b3'),\n",
       " ('b1', 'b2', 'c1'),\n",
       " ('b1', 'b2', 'c2'),\n",
       " ('b1', 'b2', 'c3'),\n",
       " ('b1', 'b3', 'c1'),\n",
       " ('b1', 'b3', 'c2'),\n",
       " ('b1', 'b3', 'c3'),\n",
       " ('b1', 'c1', 'c2'),\n",
       " ('b1', 'c1', 'c3'),\n",
       " ('b1', 'c2', 'c3'),\n",
       " ('b2', 'b3', 'c1'),\n",
       " ('b2', 'b3', 'c2'),\n",
       " ('b2', 'b3', 'c3'),\n",
       " ('b2', 'c1', 'c2'),\n",
       " ('b2', 'c1', 'c3'),\n",
       " ('b2', 'c2', 'c3'),\n",
       " ('b3', 'c1', 'c2'),\n",
       " ('b3', 'c1', 'c3'),\n",
       " ('b3', 'c2', 'c3'),\n",
       " ('c1', 'c2', 'c3')]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "standard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def desc(se):\n",
    "    ''' 값의 합이 3 배수인지 판단하는 함수'''\n",
    "    return sum(list(map(lambda a : carddic[a],se)))%3 ==0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "desc(('b3', 'c1', 'c2'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30\n"
     ]
    }
   ],
   "source": [
    "su=0\n",
    "for i in standard:\n",
    "    if desc(i):\n",
    "        su=su+1\n",
    "print(su)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "즉 해당경우는 30가지이며, 원하는 확률은 30/84 이다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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