02. Binomial Distribution.ipynb

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      "1.09 1\n",
      "0.696\n"
     ]
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   "source": [
    "def fact(n):\n",
    "    return 1 if n == 0 else n*fact(n-1)\n",
    "\n",
    "def comb(n, x):\n",
    "    return fact(n) / (fact(x) * fact(n-x))\n",
    "\n",
    "def b(x, n, p):\n",
    "    return comb(n, x) * p**x * (1-p)**(n-x)\n",
    "\n",
    "l, r = list(map(float, input().split(\" \")))\n",
    "odds = l / r\n",
    "print(round(sum([b(i, 6, odds / (1 + odds)) for i in range(3, 7)]), 3))"
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    "def fact(x):\n",
    "    return 1 if x==1 else x*fact(x-1) \n",
    "\n",
    "def comb(x, n):\n",
    "    return fact(x)/(fact(n)*fact(n-x))\n",
    "\n",
    "def b(n, x, p):\n",
    "    return comb(x, n)*p**x*(1-p)**(n-x)\n",
    "\n",
    "l, r = list(map(float, input().split(\" \")))\n",
    "\n",
    "odds = l/r\n",
    "print(round(sum([b(i, 6, odds/(1+odds)) for i in range(3, 7)]), 3))"
   ]
  },
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       "1.08"
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     "execution_count": 7,
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   "source": [
    "odds = 1.08/1\n",
    "odds"
   ]
  },
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   "cell_type": "code",
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   "metadata": {},
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     "text": [
      "12 2\n",
      "1.0\n",
      "0.014\n"
     ]
    }
   ],
   "source": [
    "def fact(n):\n",
    "    return 1 if n == 0 else n*fact(n-1)\n",
    "\n",
    "def comb(n, x):\n",
    "    return fact(n) / (fact(x) * fact(n-x))\n",
    "\n",
    "def b(x, n, p):\n",
    "    return comb(n, x) * p**x * (1-p)**(n-x)\n",
    "\n",
    "p, n = list(map(int, input().split(\" \")))\n",
    "print(round(sum([b(i, n, p/100) for i in range(3)]), 3))\n",
    "print(round(sum([b(i, n, p/100) for i in range(2, n+1)]), 3))"
   ]
  },
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   "cell_type": "raw",
   "metadata": {},
   "source": [
    "The geometric distribution is a special case of the negative binomial distribution. It deals with the number of trials required for a single success. Thus, the geometric distribution is a negative binomial distribution where the number of successes (r) is equal to 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## geometric distribution\n",
    "\n",
    "def geo(n, p):\n",
    "    return (1-p)**(n-1)*p"
   ]
  },
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   "execution_count": 10,
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       "-6144"
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     "execution_count": 10,
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   "source": [
    "geo(12, 3)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 3\n",
      "5\n",
      "0.868\n"
     ]
    }
   ],
   "source": [
    "frac=input().split(' ')\n",
    "n=int(input())\n",
    "p=int(frac[0])/int(frac[1])\n",
    "q=1-p\n",
    "prob=1-q**n\n",
    "print(round(prob,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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