{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8db3caba",
   "metadata": {},
   "source": [
    "# Ungraded Lab: Birthday Problems\n",
    "\n",
    "Welcome! During this lab you will reinforce the notion of how counter-intuitive probabilities can be by taking a look at the famous birthday problem. In fact you will take a look at 4 variations of this problem. You can use one you have already seen the solution for, to try and come up with the solution for the next one, the results might surprise you!\n",
    "\n",
    "Let's get started!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2d4d615c-0e4f-4001-a171-4d80e491e5ec",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import utils\n",
    "\n",
    "%matplotlib widget"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7958a323",
   "metadata": {},
   "source": [
    "## Introduction to the problem\n",
    "\n",
    "All of these problems share a similar setting. You have a classroom full of students (the number may vary) and want to know the probabilities of two students having the same birthday or of any student having a particular birthday, anything along those lines. As mentioned before, you will see 4 variations of the problem.\n",
    "\n",
    "You can think of these problems in two ways:\n",
    "   - What is the minimum number of students `n` that need to be in the classroom to have a matching birthday with a given probability?\n",
    "   - Given `n` what is the probability of having a match?\n",
    "    \n",
    "Both ways model the situation from different angles but they are essentially covering the same.\n",
    "\n",
    "## Play the game of matching your birthday\n",
    "\n",
    "To further motivate this situation a game is presented. You can use the following cell to run an interactive game, it is very simple to use: you need to select your birthday (the year does not matter) in the dropdown widget and then you can click the `Simulate!` button to randomly create students until one of them has the same birthday as you. The left plot shows you the history of the result for each simulation and the right plot shows you the same information in a histogram so you can see how this variable distributes.\n",
    "\n",
    "You can try this for as long as you want so you get a sense of the probability distribution for this process (it is recommended to try it for at least 30 runs):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6f450c24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2a37fe8fce804702a2bb8d33db84bb05",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "DatePicker(value=None, description='Pick your bday', step=1, style=DescriptionStyle(description_width='initial…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b69363328a5b4847a45224a8499d79e9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Simulate!', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "05db75c063c342778c5911327a6d1104",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=1000.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "game = utils.your_bday()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ec3e024",
   "metadata": {},
   "source": [
    "## First Problem\n",
    "\n",
    "The first problem tries to answer the question: given a pre-defined date, what is the value of `n` such that the probability of having a match is greater than or equal to 0.5?\n",
    "\n",
    "<img src=\"./images/first.png\" style=\"height: 200px;\"/>\n",
    "\n",
    "Before taking a look at the analytical solution you will try to solve it by creating simulations with Python. For this purpose you can use the `simulate` helper function provided in the next cell. Run it to load this function which will be used shortly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "075e35c5-85f4-427f-9d63-b540aec4caa3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def simulate(problem_func, n_students=365, n_simulations=1000):\n",
    "    \n",
    "    # Initialize the counter of matches at 0\n",
    "    matches = 0\n",
    "    \n",
    "    # Run the simulation for the desired number of times\n",
    "    for _ in range(n_simulations):\n",
    "        \n",
    "        # If there is a match in the classroom add 1 to the counter of matches\n",
    "        if problem_func(n_students):\n",
    "            matches += 1\n",
    "    \n",
    "    # Return the ratio of number of matches / number of simulations\n",
    "    return matches/n_simulations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0aa06656",
   "metadata": {},
   "source": [
    "This function returns the simulated probability for a given problem when you pass to it the number of students and the number of simulations and it has these two properties:\n",
    "\n",
    "   - The higher the number of students the higher the probability of a match.\n",
    "   - The higher the number of simulations the more accurate the simulated probability will be (This fact will be discussed further in Week 3. This is known as the Central Limit Theorem). \n",
    "\n",
    "This is pretty cool but how do you use this helper function? You need to pass another function to it that models the situation at hand. This other function should have two criteria so that `simulate` works as expected:\n",
    "\n",
    "   - It should receive the number of students as input.\n",
    "   - It should return True if there was a match or False otherwise.\n",
    "    \n",
    "You can create a function that models problem number 1 by running the following cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "14557c4f-588f-40a9-8e4e-c188b947fe42",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def problem_1(n_students):\n",
    "    \n",
    "    # Predefine a specific birthday\n",
    "    predef_bday = np.random.randint(0, 365)\n",
    "    \n",
    "    # Generate birthdays for every student\n",
    "    gen_bdays = np.random.randint(0, 365, (n_students))\n",
    "    \n",
    "    # Check if predefined bday is among students\n",
    "    return predef_bday in gen_bdays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e82157c",
   "metadata": {},
   "source": [
    "Now you can use these two functions in conjuction to get the probability of a match for a given classroom size. Notice that you can tweak the value of the `n` variable to simulate classrooms with different number of students. Also notice that this time the simulation is run 10,000 times instead of the default 1000. This gives you a more accurate simulated probability at the expense of taking longer to execute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "977e402e-58c2-45ab-9a7d-2d2095cae6d3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The simulated probability of any student to have a bday equal to a predefined value is 0.2346 in a classroom with 100 students\n"
     ]
    }
   ],
   "source": [
    "n = 100 # try changing this value!\n",
    "simulated_prob = simulate(problem_1, n_students=n, n_simulations=10_000)\n",
    "\n",
    "print(f\"The simulated probability of any student to have a bday equal to a predefined value is {simulated_prob} in a classroom with {n} students\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07ca745b",
   "metadata": {},
   "source": [
    "This is very cool but it still has one major drawback: you would need to try a bunch of values for `n` before arriving at the solution. Instead of taking this approach you can generate a plot that shows the simulated probability as a function of the number of students in the classroom:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5e201de4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a9702c6d2ab04aa8b6b46ec1ec42fc34",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=1000.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate the simulated probability for every classroom\n",
    "simulated_probs_1 = [simulate(problem_1, n_students=n) for n in utils.big_classroom_sizes]\n",
    "\n",
    "# Create a scatterplot of simulated probabilities vs classroom size\n",
    "utils.plot_simulated_probs(simulated_probs_1, utils.big_classroom_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae84cc0c",
   "metadata": {},
   "source": [
    "Remember that this approach is a simulation and thus you are generating simulated (or approximated) probabilities. Because of this the curve is not completely smooth and you will get slightly different values every time you run the simulation.\n",
    "\n",
    "## Analytical Solution\n",
    "\n",
    "Now that you have built a stronger intuition, let's calculate explicitily the probability $P$ that at least one student in the room has the birthday the same as the pre-defined date. It is clear that $P = P(n)$, i.e., the value for $P$ depends on the number of students in the room and, as $n$ become large, $P(n)$ must become closer to $1$. With a formula for $P(n)$ we can then find the minimum $n$ such that $P(n) \\geq 0.5$. Let's suppose that a year has $365$ days.\n",
    "\n",
    "Let's consider $D$ the pre-defined birthday and suppose a student is selected at random. \n",
    "\n",
    "Defining the event $S_i$ as the $i$-th student has birthday in the day $D$. Then $P(S_i) = \\frac{1}{365}$, because there are $365$ equally likely possibilities for their birthday. So, using the **complement rule**, the probability that this student's birthday isn't day $D$ is $P(S_i^c) = 1 - P(S_i) = 1 - \\frac{1}{365}$. \n",
    "\n",
    "Note that this probability is the same for any student and we can fairily assume that each student's birthday is independent from each other. Consider the event $\\mathcal{S}$ the desired event, i.e., at least one student has birthday in day $D$. Note that:\n",
    "\n",
    "$\\mathcal{S}^c$ is the probability that **no student has birthday in day $D$** and this is the same as:\n",
    "\n",
    "- Student $1$ has birthday in a day different than D, AND\n",
    "- Student $2$ has birthday in a day different than D, AND,\n",
    "...\n",
    "- Student $k$ has birthday in a day different than D.\n",
    "\n",
    "With our definitions, this is just $S_1^c \\cap S_2^c \\cap \\ldots \\cap S_k^c.$ Therefore\n",
    "\n",
    "$\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "P(\\mathcal{S}) {} & = 1 - P(\\mathcal{S}^c) \\\\\n",
    "              & = 1 - P(S_1^c \\cap S_2^c \\cap \\ldots \\cap S_k^c) \\\\\n",
    "              & = 1 - P(S_1^c)P(S_2^c) \\cdots P(S_k^c) \\text{ (independence)}\\\\\n",
    "              & = 1 - (1 - \\frac{1}{365})^n.\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "$\n",
    "\n",
    "As you've expected, $P(\\mathcal{S}) = 1 - (1 - \\frac{1}{365})^n = P(n)$. Now, you are ready to answer the question: for wich value of $n$, $P(n) \\geq \\frac{1}{2}$?\n",
    "\n",
    "Well, $P(n) \\geq \\frac{1}{2}$ is equivalent to\n",
    "\n",
    "\\begin{align}\n",
    " 1 - \\left(1 - \\frac{1}{365}\\right)^n &\\geq \\frac{1}{2} \\textit{, passing 1 to the other side and inverting the inequality sign}\\\\\n",
    "\\left(1 - \\frac{1}{365}\\right)^n &\\leq \\frac{1}{2}\\\\\n",
    "\\left(\\frac{364}{365}\\right)^n &\\leq 2^{-1} \\\\\n",
    "\\ln{\\left(\\frac{364}{365}\\right)}^n &\\leq \\ln{2^{-1}} \\\\\n",
    "n \\ln{\\left(\\frac{364}{365}\\right)} &\\leq -\\ln{2}\\\\\n",
    "\\end{align}\n",
    "\n",
    "Now, using a calculator we can easily find that $\\ln{2} \\approx 0.693$ and $\\ln{\\frac{364}{365}} \\approx -0.003$, the last inequality becomes\n",
    "\n",
    "$$n \\cdot -0.003 \\leq -0.693,$$\n",
    "\n",
    "which is equivalent to $n \\geq \\frac{0.693}{0.003} = 253$. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a326b10f",
   "metadata": {},
   "source": [
    "## Second Problem\n",
    "\n",
    "The second problem is very similar to the first one, with the difference that the predefined value is not previously defined but it is drawn from one of the students at random so it can be worded like this: given a classroom with `n` students, if you draw any student at random what is the value of `n` such that the probability of having a match with another student is greater than or equal to 0.5?\n",
    "\n",
    "<img src=\"./images/second.png\" style=\"height: 200px;\"/>\n",
    "\n",
    "You can reuse the `simulate` helper function defined earlier so the only thing left is to code the function that models this particular problem. **But before doing this try to come up with a hypothesis about the result. What do you think will happen? Will `n` be similar to the previous one or do you need a higher value? What about a smaller value?**\n",
    "\n",
    "Run the next cells to find out!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b83a13c5-812d-4637-95da-8fc4058178ec",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def problem_2(n_students):\n",
    "    \n",
    "    # Generate birthdays for every student\n",
    "    gen_bdays = np.random.randint(0, 365, (n_students))\n",
    "    \n",
    "    # Pick one student at random\n",
    "    rnd_index = np.random.randint(0, len(gen_bdays))\n",
    "    \n",
    "    # Get the bday from the selected student\n",
    "    rnd_bday = gen_bdays[rnd_index]\n",
    "    \n",
    "    # Take the bday out of the pool of bdays (otherwise there is always a match)\n",
    "    remaining_bdays = np.delete(gen_bdays, rnd_index, axis=0)\n",
    "    \n",
    "    # Check if another student shares the same bday\n",
    "    return rnd_bday in remaining_bdays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a826e6e3-be69-42b5-8995-3c13239b05ee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
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      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=1000.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate the simulated probability for every classroom\n",
    "simulated_probs_2 = [simulate(problem_2, n_students=n) for n in utils.big_classroom_sizes]\n",
    "\n",
    "# Create a scatterplot of simulated probabilities vs classroom size\n",
    "utils.plot_simulated_probs(simulated_probs_2, utils.big_classroom_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a158970e",
   "metadata": {},
   "source": [
    "## Analytical Solution\n",
    "\n",
    "Note that this problem is very similar to the first one. The difference is that, instead of selecting one day $D$ at random from the room, you select a student and fix their birthday $D$. You can reduce this problem to the previous one by removing this student from the room and considering now a room with $n-1$ students. The problem now is analogous to the previous one but you will end up with a  $n-1$ instead of $n$. Therefore, it is easy to see that, in this case,\n",
    "\n",
    "$$P(n) = 1 - \\left(1 - \\frac{1}{365} \\right)^{n-1}.$$\n",
    "\n",
    "With some calculations you get that $P(n) \\geq \\frac{1}{2}$ if and only if $n \\geq {\\frac{0.693}{0.003}} + 1 = 254$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da320d6d",
   "metadata": {},
   "source": [
    "## Third Problem\n",
    "\n",
    "The third one is the most famous of all the birthday problems and it was covered in the lectures in a sligthly different way.\n",
    "\n",
    "This time you don't want to find a match with a predefined value but rather to find a match between any two birthdays, it can be worded like this: given a classroom with students, what is the value of `n` such that the probability of having a match is greater than or equal to 0.5 for any two students?\n",
    "\n",
    "<img src=\"./images/third.png\" style=\"height: 200px;\"/>\n",
    "\n",
    "Note that, in the lectures, it was calculated the probability that **no students share a birthday**. Here, you are dealing with the case that, **at least two students share a birthday**, which is the *complement* of the question discussed in the lecture.\n",
    "\n",
    "Before doing the simulation as with previous problems ask yourself: **Do you think that the value of `n` will be similar to that of the previous problems? If you have to guess would you say it needs to be greater than or lower?**\n",
    "\n",
    "To help you out run the next cell to play an interactive version of this problem. The instructions are simple:\n",
    "\n",
    "   - To start a new simulation click anywhere on the upper panel (just below where the `Figure` headline appears)\n",
    "   - The upper panel shows randomly generated birthdays and let's you know when there is a match between two students\n",
    "   - The bottom left panel keeps track of the number of students required to have a match for every run\n",
    "   - The bottom right panel shows that same information as a histogram\n",
    "   - **Try running the simulation at least 30 times to get a sense of how this particular problem behaves**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4690bde7",
   "metadata": {},
   "outputs": [],
   "source": [
    "game_third_prob = utils.third_bday_problem()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40186804",
   "metadata": {},
   "source": [
    "Now you should have a hypothesis of the number of students in the classroom needed for the match. Test your intuition by generating the simulated probabilities as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fdc9a19c-2a85-4bae-9b57-1f3b0611da6c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def problem_3(n_students):\n",
    "    \n",
    "    # Generate birthdays for every student\n",
    "    gen_bdays = np.random.randint(0, 365, (n_students))\n",
    "    \n",
    "    # Get array containing unique bdays\n",
    "    unique_bdays = np.array(list(set(gen_bdays)))\n",
    "    \n",
    "    # Check that both the original and unique arrays have the same length \n",
    "    # (if so then no two students share the same bday)\n",
    "    return len(unique_bdays) != len(gen_bdays)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "083a603c-e5a4-4adf-a2f6-cf0045081da7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Generate the simulated probability for every classroom\n",
    "simulated_probs_3 = [simulate(problem_3, n_students=n) for n in utils.small_classroom_sizes]\n",
    "\n",
    "# Create a scatterplot of simulated probabilities vs classroom size\n",
    "utils.plot_simulated_probs(simulated_probs_3, utils.small_classroom_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9075640c",
   "metadata": {},
   "source": [
    "## Analytical solution\n",
    "\n",
    "This problem is a bit different from the previous two, so you will need to make some calculations again. Now, the idea is to perform the calculation by steps, selecting one student at time. So let's define $Q_i$ as the probability that the $i$-th student has birthday different from the previous students. Note that $Q_1 = 1$, because there is no previous student. Note also that,\n",
    "\n",
    "$$Q_2 = \\frac{364}{365}.$$\n",
    "\n",
    "This is because, given that you've selected one student, the second has $364$ possible values, it has a chance of $\\frac{364}{365}$ of not matching birthdays with the first. Now, for $Q_3$, there are $2$ selected students with different birthdays, so the probability that the third student not matches any of the previous two is:\n",
    "\n",
    "$$Q_3 = \\frac{363}{365}.$$\n",
    "\n",
    "Inductively, if we select $n$ students, then $$Q_n = \\frac{365 - (n-1)}{365}.$$\n",
    "\n",
    "Since we assume that we are choosing students independently from each other, then the probability of picking $n$ students that **don't have their birthday in common** is just the product of all $Q_n$. Let's call it $Q$, so:\n",
    "\n",
    "$$Q = Q_1 \\cdot Q_2 \\cdot \\ldots \\cdot Q_{n-1} \\cdot Q_n = 1 \\cdot \\frac{364}{365} \\cdot \\frac{363}{365} \\cdot \\ldots \\cdot \\frac{365 - (n-2)}{365} \\cdot \\frac{365 - (n-1)}{365}.$$\n",
    "\n",
    "The desired probability is, therefore, $P:= 1 - Q$, since we want the probability of **at least two students match their birthday** (this is just the complement rule).\n",
    "\n",
    "Note that we could just write a small program in Python to compute this value for every $n$ and return the first value that achieves the inequality we want ($P \\geq \\frac{1}{2}$), but for sake of completion we will provide an analytic solution.\n",
    "\n",
    "We will use the following approximation: $1 - x \\approx e^{-x}$ for $x$ small and positive. We can re-write $Q$ as\n",
    "\n",
    "$$Q = 1 \\cdot \\frac{364}{365} \\cdot \\frac{363}{365} \\cdot \\ldots \\cdot \\frac{365 - (n-2)}{365} \\cdot \\frac{365 - (n-1)}{365} \n",
    "    = \\left(1 - \\frac{1}{365} \\right) \\cdot \\left(1 - \\frac{2}{365} \\right) \\cdot \\ldots \\cdot \\left(1 - \\frac{n-2}{365} \\right) \\cdot \\left(1 - \\frac{n-1}{365} \\right).$$\n",
    "\n",
    "Thus, using the approximation:\n",
    "\n",
    "$$Q \\approx e^{-\\frac{1}{365}} \\cdot e^{-\\frac{2}{365}} \\cdot \\ldots \\cdot e^{-\\frac{n-2}{365}} \\cdot e^{-\\frac{n-1}{365}} = e^{- \\frac{1 + 2 + \\ldots + (n-1)}{365}}.$$\n",
    "\n",
    "Using the formula $1 + 2 + \\ldots + (n-1) = \\frac{n(n-1)}{2}$ (this is the sum of the first $n-1$ terms of a arithmetic progression with first term $1$ and common difference $1$), we have:\n",
    "\n",
    "$$Q \\approx e^{-\\frac{n(n-1)}{730}}.$$\n",
    "\n",
    "So, $P = 1 - Q = 1 - e^{-\\frac{n(n-1)}{730}}$ and $P \\geq \\frac{1}{2}$ is equivalent to $1 - e^{-\\frac{n(n-1)}{730}} \\geq \\frac{1}{2}$ which is equivalent to $\\frac{n(n-1)}{730} \\geq \\ln 2$, i.e., $n(n-1) \\geq 730 \\cdot \\ln 2$. Since $\\ln 2 \\approx 0.6931$, so $$n(n-1) \\geq 505.96 \\geq 505.$$\n",
    "\n",
    "Solving the quadratic equation $n(n-1) = 505$, the only positive value for $n$ is $n = \\frac{1 + \\sqrt{2021}}{2} \\approx 23.$\n",
    "\n",
    "Therefore, if $n\\geq23$ then $P \\geq \\frac{1}{2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0106c0d8",
   "metadata": {},
   "source": [
    "## Fourth Problem\n",
    "\n",
    "The fourth and final one is similar to the third problem but with the difference that you have two classrooms and want to find a match between a student in one classroom and a student in the other, presenting it like a question it will be: given two classrooms with `n` students, what is the value of `n` such that the probability of having a match is greater than or equal to 0.5 for any two students in each classroom?\n",
    "\n",
    "<img src=\"./images/fourth.png\" style=\"height: 200px;\"/>\n",
    "\n",
    "**Once again try to come up with your own hypothesis before doing the simulation!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52476294-746a-4676-b898-a5c3563a5dbd",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def problem_4(n_students):\n",
    "    \n",
    "    # Generate birthdays for every student in classroom 1\n",
    "    gen_bdays_1 = np.random.randint(0, 365, (n_students))\n",
    "    \n",
    "    # Generate birthdays for every student in classroom 2\n",
    "    gen_bdays_2 = np.random.randint(0, 365, (n_students))\n",
    "    \n",
    "    # Check for any match between both classrooms\n",
    "    return np.isin(gen_bdays_1, gen_bdays_2).any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "411889a8-317b-435a-85be-bec3f94edbf0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Generate the simulated probability for every classroom\n",
    "simulated_probs_4 = [simulate(problem_4, n_students=n) for n in utils.small_classroom_sizes]\n",
    "\n",
    "# Create a scatterplot of simulated probabilities vs classroom size\n",
    "utils.plot_simulated_probs(simulated_probs_4, utils.small_classroom_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fbc564d",
   "metadata": {},
   "source": [
    "## Analytical solution\n",
    "\n",
    "The solution to this problem is similar to the first one. Now, instead of only **one** date, there are $n$ dates to compare. \n",
    "Remember that if we have only one date $D$ to compare than the probability, let's say $Q_1$ of having **no** student with birthday $D$ is $Q_1 = (1 - \\frac{1}{365})^n$ (the complement of $P(\\mathcal{S})$ in that case). Now we proceed as problem three, by having independent samples of students. For each student sampled, the probability $Q_i$ is $(1 - \\frac{1}{365})^n$, so the probability of no student matches any of the $n$ given dates is therefore\n",
    "\n",
    "$$Q = Q_1 \\cdot Q_2 \\cdot \\ldots \\cdot Q_{n-1} \\cdot Q_n = (1 - \\frac{1}{365})^{n^2}$$\n",
    "\n",
    "Using the approximation $1 - x \\approx e^{-x}$ for $x$ small,\n",
    "\n",
    "$$Q \\approx e^{-\\frac{n^2}{365}}$$\n",
    "\n",
    "Therefore, $$P(n) \\approx 1 - e^{-\\frac{n^2}{365}}.$$ \n",
    "\n",
    "Thus, $P(n) \\geq \\frac{1}{2}$ if $n \\geq \\sqrt{\\ln 2 \\cdot 365} \\approx 15.9 \\geq 15$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1597e9d7",
   "metadata": {},
   "source": [
    "**Congratulations! You have finished the ungraded lab on the Birthday problems!**"
   ]
  }
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