{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### coin flip demo\n",
    "John Horel\n",
    "ATMOS 5340\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "enter the number of consecutive heads:  3\n"
     ]
    }
   ],
   "source": [
    "streak = input('enter the number of consecutive heads: ')\n",
    "streak = int(streak)\n",
    "prob_theory = 100. * .5 ** streak"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5, 10, 100, 1000, 10000, 100000, 1000000]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "0 5 0 0.0\n",
      "1 10 1 10.0\n",
      "2 100 10 10.0\n",
      "3 1000 126 12.6\n",
      "4 10000 1250 12.5\n",
      "5 100000 12248 12.248\n",
      "6 1000000 125053 12.5053\n"
     ]
    }
   ],
   "source": [
    "\n",
    "#unbiased coin either 0 (tail) or 1 (head)\n",
    "\n",
    "# number of times the coin is flipped\n",
    "flip_nos = [5,10,100,1000,10000,100000,1000000]\n",
    "#flip_nos = [10]\n",
    "print(flip_nos)\n",
    "#create output array for probabilities\n",
    "prob = np.zeros(7)\n",
    "print(prob)\n",
    "ctr= 0\n",
    "#loop over the different sample sizes for flipping the coin\n",
    "for flips in flip_nos:\n",
    "    no_streak = 0\n",
    "    ni=0\n",
    "    # loop over all the flips i nthe sample\n",
    "    for i in range(flips): \n",
    "        #randomly get a 0 or a 1\n",
    "        number = random.randrange(0,2)\n",
    "        #print(i,number)\n",
    "        # is it a head?\n",
    "        if number == 1:\n",
    "            ni=ni+1\n",
    "            # check whether a streak observed\n",
    "            if ni >= streak:\n",
    "                no_streak = no_streak + 1\n",
    "        else:\n",
    "            # tail. reset\n",
    "            ni=0\n",
    "    prob[ctr] = 100.*no_streak/flips\n",
    "    print(ctr,flips,no_streak,prob[ctr])\n",
    "    ctr = ctr+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 1.0, 'Theoretical Probability Unbiased Coin 12.5 %')]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,(ax1) = plt.subplots(1,1,figsize=(5,5))\n",
    "ax1.plot(prob)\n",
    "ax1.set_xticks(np.arange(len(flip_nos)))\n",
    "ax1.set_xticklabels(flip_nos)\n",
    "ax1.set(xlabel='Number of Flips',ylabel='Probability (%%)')\n",
    "ax1.set(title=\"Theoretical Probability Unbiased Coin %.1f %%\" % (prob_theory))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "atmos6010",
   "language": "python",
   "name": "u0035056"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}