{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CS 237 Spring 2021, HW 04 \n", "\n", "#### Due date: Thursday February 25th at Midnight (1 minute after 11:59pm on 2/11) via Gradescope (6 hour grace period)\n", "\n", " Late policy: You may submit the homework up to 24 hours late for a 10% penalty. Hence, the late deadline is Friday 2/26 at Midnight (with the same 6 hour grace period). \n", "\n", "#### General Instructions\n", "\n", "Please complete this notebook by filling in solutions where indicated. Be sure to \"Restart and Run All\" from the Kernel menu before submitting to Gradescope. \n", "\n", "There are 9 analytical problems and 3 programming problems. An introductory video will be posted on YT for\n", "the analytical problems, and the programming problems will be covered Friday in lab. " ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Here are some imports which will be used in code that we write for CS 237\n", "\n", "# IMPORTANT: DO NOT MAKE ANY OTHER IMPORTS WITHOUT DISCUSSING WITH PROFESSOR SNYDER\n", "\n", "# Imports used for the code in CS 237\n", "\n", "import numpy as np # arrays and functions which operate on arrays, plus math functions\n", "import matplotlib.pyplot as plt # normal plotting \n", "import math # You may use the math library if you really want, but\n", " # I recommend you use the numpy library for all mathematical operations.\n", " # Examples of use are in the notebook NumpyTutorial.ipynb on the class web site. \n", "\n", "# We will use these two functions, see note on introduction to lab problems\n", "\n", "from numpy.random import seed, random, randint, choice, shuffle\n", "\n", "from collections import Counter # Essential for creating distributions from experiments\n", " \n", "# This is an improved version of the function from HWs 01 and 02, which allows you to change the\n", "# size and also the labels on the X axis\n", "\n", "def show_distribution(outcomes, title='Probability Distribution', my_xlabels = [], my_figuresize = (8,6)):\n", " plt.figure(figsize=my_figuresize)\n", " num_trials = np.size(outcomes)\n", " X = range( int(min(outcomes)), int(max(outcomes))+1 ) # \n", " freqs = Counter(outcomes)\n", " Y = [freqs[i]/num_trials for i in X]\n", " plt.bar(X,Y,width=1.0,edgecolor='black')\n", " if my_xlabels != []:\n", " plt.xticks(X, my_xlabels)\n", " elif (X[-1] - X[0] < 30):\n", " ticks = range(X[0],X[-1]+1)\n", " plt.xticks(ticks, ticks) \n", " plt.xlabel(\"Outcomes\")\n", " plt.ylabel(\"Probability\")\n", " plt.title(title)\n", " plt.show()\n", " \n", "# Demonstration of the function\n", "dice_rolls = [ (randint(1,7) + randint(1,7)) for k in range(10**3) ] # 1000 rolls of two dice\n", "\n", "show_distribution(dice_rolls, \"Probability Distribution for $10^3$ Dice Rolls\") # notice the Latex in the title!\n", "\n", "show_distribution([ (x % 2) for x in dice_rolls ], \n", " \"Probability Distribution of Even and Odd Rolls\", \n", " my_xlabels=['Even', 'Odd'], my_figuresize=(4,4) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytical Problems \n", "\n", "You may use ordinary ASCII text to write your solutions, or (preferably) Latex. A nice video introduction to Markdown Cellls and Latex in Jupyter notebooks may be found here.\n", "Various complicated examples are shown with Latex here. \n", "\n", "You may use fractions throughout your calculations, and answers may be given as fractions if very simple, but in general I want you to give them in decimal form. \n", "\n", "Such answers must be given as decimals to 4 significant digits, unless very small, in which case you should give in scientific notation to 4 significant digits. Code for calculating this was shown in HW 03. \n", "\n", "You may present your answers in Markdown or Code cells. You are free to create extra Code cells to do the\n", "calculations. Just make sure to indicate clearly where your answer is; one nice way to do this, in the case of numeric answers, is to put it in a box:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is my answer, graders: $\\boxed{3.1416}$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 1\n", "\n", "Suppose you flip an unfair coin 3 times, where the chance of head is 0.6 and the chance of tails is 0.4, and you count the number of heads\n", "showing. Let A = \"the number of heads showing is odd\" and B = \"the number of heads showing is greater than 1.\" \n", "\n", "(A) Analyze as in HW 02. In this case, it is useful to give the \"pre-sample\n", "space\" (the three outcomes for each coin, e.g., HTH). \n", "\n", "\n", "(B) What is the probability $P(A|B)$?\n", "\n", "Show all work for full credit. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A six-sided die (with numbers 1 .. 6 on its faces) is loaded in such a way that each even-numbered face is twice as likely as each odd-numbered face. All even faces are equally likely, and all odd faces are equally likely.\n", "\n", "The die is rolled once. Let A = \"the outcome is at least 2,\" and B = \"the come is less than 4.\"\n", "\n", " Analyze this random experiment. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:** \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose 2 cards are drawn without replacement (the usual situation with cards) from an ordinary deck of 52 randomly shuffled cards. Find the probability that:\n", "\n", "(A) The first card is not a ten of clubs or an ace;\n", "\n", "(B) The first card is an ace, but the second is not;\n", "\n", "(C) The cards have the same denomination (i.e., both are Aces, both are 2's, both are 3's, etc.);\n", "\n", "(D) At least one card is a diamond;\n", "\n", "(E) Not more than 1 card is a picture card (Jack, Queen, King).\n", "\n", "Show all work for full credit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 4\n", "\n", "Suppose we have two events $A$ and $B$. For each of these five cases, give the value or the simplest formula for $P(A\\vert B)$:\n", "\n", "(A) $A\\cap B = \\emptyset$ ($A$ and $B$ are disjoint)\n", "\n", "(B) $A \\subseteq B$\n", "\n", "(C) $B \\subseteq A$\n", "\n", "(D) $A = S$ (the whole sample space)\n", "\n", "(E) $B = S$ (the whole sample space)\n", "\n", "Show all work for full credit (the formulae should be very simple). " ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "**Solution:**\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 5\n", "\n", "A faulty communication line for digital signals changes 1/4 of the 0's to 1's and 1/3 of the 1's to 0's. If 40% of a\n", "particular file being transmitted consists of 0's and 60% consists of 1's, what is the probability that when a 0 is received it was\n", "transmitted correctly? Show all work for full credit. A diagram will help with your analysis, but you do not need to show it in your answer. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 6\n", "\n", "You have two bags of colored balls. Bag A contains 3 red and 2 black balls;\n", "and Bag B contains 1 red ball and 5 black balls. Both bags are shaken so that they\n", "are in random order but the bags are kept separate. \n", "\n", "Answer each of the following questions, showing all relevant calculations. \n", "If necessary, analyze these using a tree diagram, but no need to show the diagram\n", "in your answer. \n", "\n", "\n", "(A) Suppose you draw a ball from Bag A and find it is red; then you draw a ball from Bag B and\n", "find that it is black; you throw all the *remaining* balls from both bags into a third bag, shake it, and\n", "draw a ball. What is the probability that it is black?\n", "\n", "(B) Suppose you draw a ball from Bag A and a ball from Bag B and\n", "find that they are the same color; you throw all the *remaining* balls from both bags into a third bag, shake it, and\n", "draw a ball. What is the probability that it is black?\n", "\n", "(C) Suppose you flip an unfair coin, where the probability of heads is 0.7 and choose bag A if you get heads,\n", "and bag B if you get tails, and then draw one ball. What is the probability that it is red?\n", "\n", "(D) Suppose you tell a friend to flip a fair coin to choose one of the bags, and then draw\n", "a ball without telling you which bag it came from; you see that it is red. \n", "What is the probability that it came from Bag A? " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 7\n", "\n", "For three events A, B, and C, we know that\n", "\n", " - A and C are independent,\n", " - B and C are independent,\n", " - A and B are disjoint,\n", "\n", "Furthermore, suppose that $P(A\\cup C)\\, =\\, \\frac{2}{3},\\, P(B\\cup C)\\,=\\,\\frac{3}{4},\\, P(A\\cup B\\cup C)\\,=\\,\\frac{11}{12}.$ \n", "\n", "Find $P(A)$, $P(B)$, and $P(C)$.\n", "\n", "Show all work for full credit. A diagram might be helpful, but you do not need to show it in your solution. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 8\n", "\n", "A sack contains 100 coins, of which we know that 99 are fair coins, and one is a trick coin with two heads. \n", "\n", "(A) Suppose we choose 4 coins from the sack (without replacement). What is the probability that we will choose a double-headed coin among the 4?\n", "\n", "(B) Suppose we choose a coin from the sack and flip it. What is the probability that it will land heads?\n", "\n", "(C) Suppose we choose a coin from the sack and flip it 7 times, and it lands heads all 7 times. What is the probability that it was a double-headed coin?\n", "\n", "Show all work for full credit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 9 \n", "\n", "The Jack of Spades, Jack of Hearts, Queen of Spades, and Queen of Hearts are taken from a deck of cards. The 48 remaining cards are set aside, and the four cards are shuffled and two cards are selected from the \"4-card deck\" (without replacement). \n", "\n", " All these problems are to be considered separately. Let Q = \"both cards are Queens.\"\n", "\n", "(A) Suppose the first card is a Queen, what is P(Q)? \n", "\n", "(B) Suppose that the second card drawn is a Queen, but you don't know what the first card is. Now what is P(Q)? (So, the point is, is this different from A?)\n", "\n", "(C) Suppose at least one of the cards is a Queen. Now what is P(Q)?\n", "\n", "(D) Suppose that one of the cards is the Queen of Spades. Now what is P(Q)?\n", "\n", "(E) Suppose when you draw the first card you throw it away without looking at it. You don't know what it was. What is the probability that the second card is a Queen? (Note that this is NOT the same problem as (B).)\n", "\n", "Show all work for full credit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lab Problems\n", "\n", "One of the main themes in the lab problems have been the simulation of various kinds of random processes using Python, and writing our own versions of some useful random number functions from `numpy`. We will continue in the same direction this week, creating a useful function to effectively do coin flips, and then creating a useful variation of the choice function\n", "from last lab. One feature we will incorporate in these functions is the ability to\n", "simulate non-equiprobable sample spaces, such as when we have an unfair coin. \n", "\n", "We will then use these to perform several non-trivial experiments. Finally, in our last problem we will have a warm-up to next week's lectures and lab on Poker Probabilities. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 10: Flipping an unfair coin\n", "\n", "In order to simulate a fair coin, it is sufficent to generate 0's and 1's with equal probability using `randint(...)`:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Flip a fair coin and count the number of heads showing\n", "# Run this cell a few times to get the idea\n", "\n", "randint(2)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 1, 1, 0, 0, 0, 1, 1, 1, 1])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# You can also generate an array of such flips\n", "# Run this cell a few times to get the idea\n", "\n", "randint(2,size=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, how do we simulate an unfair coin? If the probability of heads is $p$,\n", "where $p$ is an arbitrary floating-point number between $0$ and $1$, this can not\n", "be done with `randint(...)` in the way just described. \n", "\n", "The solution to this is to use the `random()` function to generate a random\n", "number in the range $[0..1)$ and then compare it with $p$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (A)\n", "\n", "Complete the following template and test it as shown" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "None\n", "None\n" ] } ], "source": [ "# Generate a 1 with probability $p$ and a 0 with probability $1-p$ \n", "# As with last week's lab, if size == None, generate a single value,\n", "# otherwise generate of list of that size. \n", "\n", "# You must use random() to implement this function. \n", "\n", "def flipCoin(p,size=None):\n", " pass # Your code here\n", " \n", "seed(0)\n", "\n", "print(flipCoin(0.5)) # should print: 0\n", "\n", "print(flipCoin(0.65,size=10)) # should print: [0, 1, 1, 1, 1, 1, 0, 0, 1, 0]" ] }, { "attachments": { "Screen%20Shot%202021-02-18%20at%208.31.26%20PM.png": { "image/png": "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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### Part (B)\n", "\n", "Now you should verify the result shown in the very first lecture: if you flip\n", "a coin a large number of times, the average number of heads should approach $p$ (the probability of heads).\n", "\n", "What to do: \n", "\n", "- Generate a sequence of $5,000$ coin flips using `flipCoin(...)` with $p= 0.65$; \n", "- Calculate the average number of heads after 10, 20, 30, ..., 5,000 flips (you will have a list of 500 numbers);\n", "- Plot these values to obtain the following illustration (refer to the PythonFor237 notebook if you forget how to do plots). \n", "\n", "![Screen%20Shot%202021-02-18%20at%208.31.26%20PM.png](attachment:Screen%20Shot%202021-02-18%20at%208.31.26%20PM.png)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# Your solution\n", "seed(0)\n", "p = 0.65\n", "num_trials = 5000\n", "\n", "pass # Your code here\n", "\n", "# Hint: use plt.xlim(0,1) to make sure the y axis includes the whole range 0..1. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 11: Choosing Non-Equiprobably\n", "\n", "The `choice` function from `numpy` which we simulated in the last lab\n", "has an additional parameter which we did not simulate, which allows you to\n", "specify the probabilities of the various elements in the list, which of course\n", "is necessary if the elements are not equiprobable. Effectively, the list chosen from is the sample space, and the list of probabilities is the probability function (as when we **Analyzed**\n", "problems in the last homework). This is really only useful if the choice is done *with replacement* and if the probabilities in $p$ sum to 1.0. If $p$ = None, then the choice is made equiprobably. \n", "\n", "The following code cell illustrates this features. You can read in detail about `choice` here. " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Try this a few times and observe that numbers are generated\n", "# non-equiprobably\n", "\n", "choice([1,2,3])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2, 1, 2, 2, 3, 1, 3, 1, 1, 1, 3, 2, 3, 3, 1, 2, 2, 2, 2, 1])" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Try a few times and again observe that this is equiprobable\n", "\n", "choice([1,2,3],size=20)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Try this a few times and observe that numbers are generated\n", "# non-equiprobably\n", "\n", "choice([1,2,3],size=None,p=[0.1,0.3,0.6])" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 3, 3, 3, 3, 3, 3, 3, 1, 3, 1, 3, 3, 3, 1, 3, 3, 3, 0, 3])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Try this a few times and observe that numbers are generated\n", "# non-equiprobably\n", "\n", "choice([0,1,3],size=20,p=[0.1,0.3,0.6])" ] }, { "attachments": { "Screen%20Shot%202021-02-19%20at%201.50.06%20AM.png": { "image/png": "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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### Part (A)\n", "\n", "Now you will implement your own version of `choice` (with replacement) by completing the following template.\n", "\n", "NOTE: You do NOT have to implement the `replace` parameter, and should assume that\n", "the function always chooses WITH replacement.\n", "\n", "Hint: This is similar to the way you implemented the `flipCoin` function above, but\n", "with a list of probabilities. Generate a random value `r` in the range $[0..1)$\n", "and then successively add the values in `p` until you equal or exceed `r`. \n", "You are effectively dividing the line $[0..1)$ into regions corresponding\n", "to the various probabilities (length == probability). \n", "\n", "For example, if you have X = [0,1,3] and p = [0.1,0.3,0.6], then you can diagram\n", "the probabilities as follows:\n", "\n", "![Screen%20Shot%202021-02-19%20at%201.50.06%20AM.png](attachment:Screen%20Shot%202021-02-19%20at%201.50.06%20AM.png)\n", "\n", "\n", "\n", "- If you generate r = 0.26 then you would return 1, because as you scan from the left, r > 0.1, but r <= 0.1 + 0.3 = 0.4; \n", "\n", "- If you generate r = 0.679 then you would return 3, because as you scan from the left, r > 0.1, and r > 0.1 + 0.3 = 0.4, but r <= 0.1 + 0.3 + 0.6 = 1.0. \n", "\n", "The effect of this is that you are selecting a random point in the interval, and finding out which region it lands in, where the\n", "length of each region is the probability. " ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "None None None None\n", "None None None None\n" ] } ], "source": [ "# Choose a single element of X according to p = None (equiprobably) or p = list of probs\n", "# You may assume that len(X) = len(p)\n", "\n", "def choose1(X,p=None):\n", " pass # Your code here\n", " \n", "# Now implement the main function, using choose1(...)\n", "\n", "def my_choice(X,size=None,p=None):\n", " pass # Your code here\n", "\n", "# test it\n", "\n", "seed(0)\n", "\n", "X = [1,2,3,4,5,6]\n", "\n", "print( choose1(X), choose1(X), choose1(X), choose1(X) ) # should print 5 6 1 4\n", "\n", "p = [0.1,0.1,0.1,0.2,0.2,0.3]\n", "print( choose1(X,p), choose1(X,p), choose1(X,p), choose1(X,p) ) # should print 6 6 5 4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (B)\n", "\n", "Show the distribution for the problem of rolling a fair die and\n", "observing the number of dots showing. This should be a familiar shape! Use `my_choice` and $10^5$ trials. \n", "\n", "Hint: `show_distribution` is provided in the first code cell of the notebook. " ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# Show the distribution of a fair die over 10^5 trials\n", "\n", "seed(0)\n", "\n", "pass # Your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (C)\n", "\n", "Do a simulation of the experiment described in Problem 1 above for $10^5$ trials, using your `my_choice` function\n", "with the probability space and probability function as determined in Problem 1, and display the probability distribution using `show_distribution`. " ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "# Solution (B)\n", "\n", "seed(0)\n", "\n", "pass # Your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (D)\n", "\n", "Show the distribution for the problem of rolling two fair dice and\n", "counting the number of dots showing. This should also be a familiar shape! Use `my_choice` and $10^5$ trials. \n", "\n", "Hint: `show_distribution` is provided in the first code cell of the notebook." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "scrolled": false }, "outputs": [], "source": [ "# Show the distribution of sum of two fair dice over 10^5 trials\n", "\n", "seed(0)\n", "\n", "pass # Your code here" ] }, { "attachments": { "PlayingCards.png": { "image/png": "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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### Problem 12: Simulation of Card Games\n", "\n", "This is a \"warm-up\" for next week's lectures and lab, where we will calculate the probability of all the common Poker\n", "Hands and verify them experimentally. \n", "\n", "Card games generally start by shuffling a deck (randomizing it) and then dealing\n", "out a *hand* of $n$ cards. In this problem we will investigate how to\n", "do such simulations efficiently. In poker, hands are 5 cards, but other games involve\n", "other sizes of hands. \n", "\n", "In order to do this efficiently, we need to encode all the information using integers, and the experiments will involve only counting how many instances of an event (such as\n", "\"the hand consists of 5 cards of the same suit\") occur and calculating the probability. \n", "\n", "NOTE: For this problem, since we need to choose **without replacement** we will not use\n", "our `my_choice` from above, but the `numpy` function `choice`. \n", "\n", "The deck of playing cards:\n", "\n", "![PlayingCards.png](attachment:PlayingCards.png)\n", "\n", "will be represented simply by small integers $0,\\ldots , 51,$ corresponding to\n", "counting the cards across and then down the rows. \n", "\n", "\n", "| | A (1) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | J (11) | Q (12) | K (13) | |\n", "|----------|---|---|---|---|---|---|---|---|---|----|---|---|---|:---|\n", "| Spades (0) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Black (1) |\n", "| Hearts (1) | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | Red (0) |\n", "| Diamonds (2)| 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | Red (0) |\n", "| Clubs (3) | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | Black (1) |\n", "\n", "For efficiency, we will encode everything as integers, as shown above:\n", "\n", "- Cards are integers in the range [0..51]\n", "- Denominations: Ace = 1, 2 = 2, ..., 10 = 10, Jack = 11, Queen = 12, King = 13\n", "- Suits: Spade = 0, Heart = 1, Diamond = 2, Club = 3\n", "- Colors: Red = 0, Black = 1\n", "\n", "The following code cell provides convenient ways to \"pretty print\" the cards\n", "if necessary. In general we will not need these for the experiments, they\n", "are useful for debugging and illustration. \n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['AS' '2S' '3S' '4S' '5S' '6S' '7S' '8S' '9S' '10S' 'JS' 'QS' 'KS' 'AH'\n", " '2H' '3H' '4H' '5H' '6H' '7H' '8H' '9H' '10H' 'JH' 'QH' 'KH' 'AD' '2D'\n", " '3D' '4D' '5D' '6D' '7D' '8D' '9D' '10D' 'JD' 'QD' 'KD' 'AC' '2C' '3C'\n", " '4C' '5C' '6C' '7C' '8C' '9C' '10C' 'JC' 'QC' 'KC']\n", "\n", "34 9D\n", "\n", "[ JH 7C QS 9S QC ]\n" ] } ], "source": [ "# Denominations are 1 = A, 2 = 2, ...., 10 = 10, 11 = Jack, 12 = Queen, 13 = King\n", "# None is added at index 0 to line up with array indices. \n", " \n", "Denomination = np.array( [None,'A','2','3','4','5','6','7','8','9','10','J','Q','K'] )\n", "\n", "# Suits 'S' = Spades, 'H' = Hearts, 'D' = Diamonds, 'C' = Clubs \n", "Suit = np.array( ['S', 'H', 'D', 'C'] )\n", " \n", "Color = np.array( ['R','B'] )\n", " \n", "# List comprehensions are a great way to avoid explicit for loops when creating lists\n", "\n", "Deck = np.array( [(d+s) for s in Suit for d in Denomination[1:]] ) # Note the double for loop\n", "\n", "def printHand(hand):\n", " s = \"[ \"\n", " for h in hand:\n", " s += Deck[h] + ' '\n", " print(s+ \"]\")\n", "\n", "# Examples\n", "\n", "print( Deck )\n", "print()\n", "\n", "print(34,Deck[34])\n", "print()\n", "\n", "printHand([23,45,11,8,50])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (A)\n", "\n", "The first task is to write functions which can take a card (a number in [0 .. 51])\n", "and return the denomination (integers in [1,..,13]), the rank(integers in [0,..,3]),\n", "or the color (0 or 1). \n", "\n", "You may NOT implement this by creating lists and simply using the card number to index into this list, you must calculate it using comparisons or simple arithmetic functions % and //. \n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[None 'A' '2' '3' '4' '5' '6' '7' '8' '9' '10' 'J' 'Q' 'K']] [['S' 'H' 'D' 'C']] AS [['R' 'B']]\n", "[[None 'A' '2' '3' '4' '5' '6' '7' '8' '9' '10' 'J' 'Q' 'K']] [['S' 'H' 'D' 'C']] 7H [['R' 'B']]\n", "[[None 'A' '2' '3' '4' '5' '6' '7' '8' '9' '10' 'J' 'Q' 'K']] [['S' 'H' 'D' 'C']] 9D [['R' 'B']]\n", "[[None 'A' '2' '3' '4' '5' '6' '7' '8' '9' '10' 'J' 'Q' 'K']] [['S' 'H' 'D' 'C']] JC [['R' 'B']]\n" ] } ], "source": [ "# Denomination is just column number + 1: 1 = Ace, 2 = 2, etc. , 11 = J, 12 = Q, 13 = K\n", "\n", "def denom(card):\n", " pass # Your code here\n", "\n", "# Suits are just row numbers: 0 = Spades; 1 = Hearts; 2 = Diamonds; 3 = Clubs\n", "\n", "def suit(card):\n", " pass # Your code here\n", "\n", "# Colors: 0 = Red, 1 = Black\n", "\n", "def color(card):\n", " pass # Your code here\n", "\n", "# Test them!\n", "\n", "print(Denomination[denom(0)],Suit[suit(0)],\n", " Deck[0], Color[color(0)]) # should print A S AS B\n", "\n", "print(Denomination[denom(19)],Suit[suit(19)],\n", " Deck[19], Color[color(19)]) # should print 7 H 7H R\n", "\n", "print(Denomination[denom(34)],Suit[suit(34)],\n", " Deck[34], Color[color(34)]) # should print 9 D 9D R\n", "\n", "print(Denomination[denom(49)],Suit[suit(49)],\n", " Deck[49], Color[color(49)]) # should print J C JC B" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the following, you should use the `numpy` function `choice` (you wrote your own version last time, but from here forward, you should use the `numpy` version). You can't use\n", "`my_choice` from above, because we need to choose equiprobably and **without replacement**. \n", "\n", "You can read about `choice` here, in case you forgot what you did in the last HW ! \n", "\n", "Hint: Don't forget about the `replace` parameter!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (B)\n", "\n", "Now you must write a simulation of the following experiment: \n", "\n", "> Suppose you draw 7 cards (without replacement, as usual in card games); what is the probability that \n", "3 of the cards are Red and 4 are Black?\n", "\n", "Perform the experiment for $10^5$ trials and report your answer. \n", "\n", "Hint: There is a simple way to convert each hand into colors and determine whether\n", "3 are Red and 4 are Black, if you understand how colors are represented. \n", "\n", "You might find the Python function `sum` useful (it returns the sum of a list of numbers). " ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability that 3 cards are Red and 4 Black is None\n" ] } ], "source": [ "num_trials = 10**5\n", "\n", "N = 7\n", "\n", "seed(0)\n", "\n", "pass # Your code here\n", "\n", "# The exact probability is 0.29054174861433935, you should get 0.2896\n", "\n", "print(\"The probability that 3 cards are Red and 4 Black is\", None) # replace with your answer\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (C)\n", "\n", "Now we will verify an analytical result from HW 03, Problem 10 (C). \n", "\n", "Write a simulation, using $10^5$ trials, to answer the following\n", "question:\n", "\n", "> Suppose you draw 2 cards without replacement from a standard deck of playing cards. What is the probability that the two cards were different colors?\n", "\n", "Hint: You can cut and paste the previous answer and make some minimal changes, if you\n", "wrote the previous part correctly!" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability that the 2 cards were different colors is None\n" ] } ], "source": [ "num_trials = 10**5\n", "\n", "N = 2\n", "\n", "seed(0)\n", "\n", "pass # Your code here\n", "\n", "# The exact probability is 0.5098039215686274, you should get 0.511\n", "\n", "print(\"The probability that the 2 cards were different colors is\", None) # replace with your answer\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (D)\n", "\n", "Now we will verify an analytical result from HW 03, Problem 10 (B). \n", "\n", "Write a simulation, using $10^5$ trials to answer the following\n", "question:\n", "\n", "> Suppose you draw 2 cards without replacement from a standard deck of playing cards. What is the probability that the first card was red and the second card was a face card?\n" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability that the first card was red and the second card was a face card is None\n" ] } ], "source": [ "\n", "num_trials = 10**5\n", "\n", "N = 2\n", "\n", "seed(0)\n", "\n", "pass # Your code here\n", "\n", "# The exact probability is 0.11538461538461539, you should get 0.1169\n", "\n", "print(\"The probability that the first card was red and the second card was a face card is\", None) # replace with your answer\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (E)\n", "\n", "Finally, we will think about a problem in Poker Probabilities, which we will continue to\n", "think about in our next lab, where we will verify experimentally our analysis of\n", "the probabilities of Poker hands from our study of combinatorics. \n", "\n", "As a warmup to next week, we will determine the probability that when you are dealt\n", "5 cards, you get a Flush, which is (here) defined as a hand consisting of 5 cards of exactly the same suit. (Technically, in Poker a Flush means five of the same suit, but\n", "not a Straight Flush or a Royal Flush, but we will use a simpler definition.)\n", "\n", "Write a simulation, using $10^5$ trials to answer the following\n", "question:\n", "\n", "> Suppose you draw 5 cards without replacement from a standard deck of playing cards. What is the probability that all the cards are the same suit?\n", " \n", "Hint: convert each hand into a list of suits, and then check that all the suits\n", "are the same. " ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability that the hand was a Flush is None\n" ] } ], "source": [ "num_trials = 10**5\n", "\n", "N = 5\n", "\n", "seed(0)\n", "\n", "pass # Your code here\n", "\n", "# The exact probability is 0.0019807923169267707, you should get 0.002 \n", "\n", "print(\"The probability that the hand was a Flush is\", None) # replace with your answer\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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }