chapter_4/poker_test_four_digit.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "each random number is of `four digits`. The following combination are possible:\n",
    "(a) Four different digits  <br>\n",
    "(b) One pair in the digits  <br>\n",
    "(c) Two pairs  <br>\n",
    "(d) Three digits of one kind   <br>\n",
    "(e) All four digits of one kind.  <br>\n",
    "\n",
    "The probability of occurrence of combination (a), that is four different digits is, <br>\n",
    "P (a) = 0.9 x .8 x .7 = 0.504 <br>\n",
    "The probability having one pair and the other two different digits is,  <br>\n",
    "P (b) =(4/2) *.1 × .9 × .8 = 0.432 <br>\n",
    "The probability of having two pairs of like digits is, <br>\n",
    "P(c)= (4/2)*.1 x .1 x.9= 0.054 <br>\n",
    "The probability of having three digits of a kind is,  <br>\n",
    "P(d)= 0.1 x .1 x .9 = 0.009 <br>\n",
    "The probability of having all four digits of one kind is <br>\n",
    "P(e) = 0.1 * .1 * .1 = .001 <br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import scipy.stats as stats\n",
    "\n",
    "\n",
    "# def generate_random_number():\n",
    "#     return random.randint(1000, 9999)\n",
    "# # Generate a sequence of 10,000 random four-digit numbers\n",
    "# random_numbers = [generate_random_number() for _ in range(10000)]\n",
    "\n",
    "observed_frequencies = {\n",
    "    'Four different digits': 5120,\n",
    "    'One pair in the digits': 4230,\n",
    "    'Two pairs': 560,\n",
    "    'Three digits of one kind': 75,\n",
    "    'All four digits of one kind': 15\n",
    "}\n",
    "\n",
    "total_numbers = sum(observed_frequencies.values())\n",
    "\n",
    "\n",
    "# if random number not given in question\n",
    "# total_numbers = len(random_numbers)\n",
    "# for num in random_numbers:\n",
    "#     digits = [int(d) for d in str(num)]\n",
    "#     digit_counts = [digits.count(d) for d in set(digits)]\n",
    "\n",
    "#     if len(set(digits)) == 4:\n",
    "#         observed_frequencies['Four different digits'] += 1\n",
    "#     elif 2 in digit_counts:\n",
    "#         observed_frequencies['One pair in the digits'] += 1\n",
    "#     elif digit_counts.count(2) == 2:\n",
    "#         observed_frequencies['Two pairs'] += 1\n",
    "#     elif 3 in digit_counts:\n",
    "#         observed_frequencies['Three digits of one kind'] += 1\n",
    "#     elif all(count == 4 for count in digit_counts):\n",
    "#         observed_frequencies['All four digits of one kind'] += 1\n",
    "\n",
    "print(\"Observed frequencies:\")\n",
    "for combination, count in observed_frequencies.items():\n",
    "    print(f\"{combination}: {count} ({count / total_numbers * 100:.2f}%)\")\n",
    "\n",
    "expected_frequencies = {\n",
    "    'Four different digits': total_numbers * 0.504,\n",
    "    'One pair in the digits': total_numbers * 0.432,\n",
    "    'Two pairs': total_numbers * 0.054,\n",
    "    'Three digits of one kind': total_numbers * 0.009,\n",
    "    'All four digits of one kind': total_numbers * 0.001\n",
    "}\n",
    "\n",
    "print(\"===\")\n",
    "print(expected_frequencies)\n",
    "print(\"===\")\n",
    "\n",
    "chi_square = 0\n",
    "for combination in observed_frequencies:\n",
    "    observed = observed_frequencies[combination]\n",
    "    expected = expected_frequencies[combination]\n",
    "    chi_square += (observed - expected) ** 2 / expected\n",
    "\n",
    "print(\"Chi-square statistic:\", chi_square)\n",
    "\n",
    "# Compare chi_square value with critical chi-square value at desired significance level\n",
    "# Degrees of freedom for the chi-square test\n",
    "df = len(observed_frequencies) - 1\n",
    "\n",
    "# Significance level (alpha)\n",
    "alpha = 0.05\n",
    "\n",
    "# Critical chi-square value\n",
    "critical_chi_square = stats.chi2.ppf(1 - alpha, df)\n",
    "\n",
    "if chi_square > critical_chi_square:\n",
    "    print(\"Reject the null hypothesis. The random numbers are not independent.\")\n",
    "else:\n",
    "    print(\"Not reject the null hypothesis. The random numbers are independent.\")\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}