{
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  {
   "cell_type": "markdown",
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   "source": [
    "### Drawing cards\n",
    "\n",
    "NOTE: In this notebook I use the `stats` sub-module of `scipy` for all statistics functions, including generation of random numbers. There are other modules with some overlapping functionality, e.g., the regular python random module, and the `scipy.random` module, but I do not use them here. The `stats` sub-module includes tools for a large number of distributions, it includes a large and growing set of statistical functions, and there is a unified class structure. (And namespace issues are minimized.) See https://docs.scipy.org/doc/scipy/reference/stats.html."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Intro\n",
    "\n",
    "For each of the draws, the probability of getting a heart is $\\frac{1}{4}$.  The probability of getting $k$ successes in $n$ independent trials, where the $p$ is the probability of success in an indvidual trial is given by the binomial distribution `stats.binom.pmf(k,n,p)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of 0 hearts is 0.17797851562499994\n",
      "The probability of 1 hearts is 0.35595703125\n",
      "The probability of 2 hearts is 0.296630859375\n",
      "The probability of 3 hearts is 0.13183593749999992\n",
      "The probability of 4 hearts is 0.03295898437499997\n",
      "The probability of 5 hearts is 0.004394531250000001\n",
      "The probability of 6 hearts is 0.000244140625\n"
     ]
    }
   ],
   "source": [
    "for k in range(7):\n",
    "    n = 6\n",
    "    p = 0.25\n",
    "    print(\"The probability of\",k,\"hearts is\", stats.binom.pmf(k,n,p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Version information\n",
    "`version_information` is from J.R. Johansson (jrjohansson at gmail.com); see <a href='http://nbviewer.jupyter.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-0-Scientific-Computing-with-Python.ipynb'>Introduction to scientific computing with Python</a> for more information and instructions for package installation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext version_information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.11.5 64bit [MSC v.1916 64 bit (AMD64)]"
        },
        {
         "module": "IPython",
         "version": "8.15.0"
        },
        {
         "module": "OS",
         "version": "Windows 10 10.0.26100 SP0"
        },
        {
         "module": "scipy",
         "version": "1.11.1"
        },
        {
         "module": "matplotlib",
         "version": "3.7.2"
        }
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      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.11.5 64bit [MSC v.1916 64 bit (AMD64)]</td></tr><tr><td>IPython</td><td>8.15.0</td></tr><tr><td>OS</td><td>Windows 10 10.0.26100 SP0</td></tr><tr><td>scipy</td><td>1.11.1</td></tr><tr><td>matplotlib</td><td>3.7.2</td></tr><tr><td colspan='2'>Sat Feb 08 14:44:35 2025 Eastern Standard Time</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.11.5 64bit [MSC v.1916 64 bit (AMD64)] \\\\ \\hline\n",
       "IPython & 8.15.0 \\\\ \\hline\n",
       "OS & Windows 10 10.0.26100 SP0 \\\\ \\hline\n",
       "scipy & 1.11.1 \\\\ \\hline\n",
       "matplotlib & 3.7.2 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Sat Feb 08 14:44:35 2025 Eastern Standard Time} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.11.5 64bit [MSC v.1916 64 bit (AMD64)]\n",
       "IPython 8.15.0\n",
       "OS Windows 10 10.0.26100 SP0\n",
       "scipy 1.11.1\n",
       "matplotlib 3.7.2\n",
       "Sat Feb 08 14:44:35 2025 Eastern Standard Time"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "version_information scipy, matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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