evenement_ensemble_probabilite_bacpro.ipynb

evenement_ensemble_probabilite_bacpro.ipynb

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      "source": [
        "<a href=\"https://colab.research.google.com/gist/jeanpat/e2aba1da2974407b691abf6b843ecd98/evenement_ensemble_probabilite_bacpro.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Evenements, ensembles et probabilités.\n",
        "Utilisation de Python pour aborder les opérations ensemblistes."
      ],
      "metadata": {
        "id": "AsNauejN07kY"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ejczUnhNswV5"
      },
      "source": [
        "## Commençons par importer quelques modules:\n",
        "   * Si possible Diagrammes de Venn (Sans doute pas disponible dans Capytale).\n",
        "   * pyplot, on ne sait jamais...\n",
        "   * le module Fraction, pour avoir des valeurs exactes pour les probabilités, ce qui est plus agréable.\n",
        "   "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "51RjKvWIrree"
      },
      "outputs": [],
      "source": [
        "from matplotlib_venn import venn3\n",
        "from matplotlib import pyplot as plt\n",
        "from fractions import Fraction"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YQczJFaMv4EP"
      },
      "source": [
        "# Définissons trois types de paquets de cartes correspondants aux ensembles:\n",
        "\n",
        "  * Un ensemble $A$ comprenant 7 cartes: $$\\large{A = \\{roi,dame,sept,as,dix,six,valet\\}}$$\n",
        "  * Un ensemble $B$ comprenant 3 cartes: $$\\large{B = \\{dame,deux,dix\\} }$$\n",
        "  * Un ensemble $C$ comprenant 3 cartes: $$\\large{C = \\{trois, quatre, cinq\\} }$$\n",
        "\n",
        "ainsi que l'ensemble $U$ réunion des ensembles $A$, $B$ et $C$\n",
        "\n",
        "$$\\huge{U= A \\cup B \\cup C}$$\n",
        "\n",
        "Dit autrement, $U$ est l'ensemble des cartes disponibles, ce sera notre **univers**.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fJhTCn2-yBdX"
      },
      "outputs": [],
      "source": [
        "A = {'roi','dame','sept','as','dix','six','valet'}\n",
        "B = {'dame','deux','dix'}\n",
        "C = {'trois','quatre','cinq'}\n",
        "U = A | B | C"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SHehlqCbyWUk"
      },
      "source": [
        "Vérifions le type de $U$ : c'est un ensemble (set)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_dV3Td-LrPCV",
        "outputId": "a114a1a3-a70e-4654-b9a4-f8c3bb4ce5cd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "set"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "type(U)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C-V0pOnWyf8P"
      },
      "source": [
        "Quels sont les éléments de $U$?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J7nOkDhMrPCo",
        "outputId": "8122e32a-d721-4cc8-809e-949bcde813de"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'as',\n",
              " 'cinq',\n",
              " 'dame',\n",
              " 'deux',\n",
              " 'dix',\n",
              " 'quatre',\n",
              " 'roi',\n",
              " 'sept',\n",
              " 'six',\n",
              " 'trois',\n",
              " 'valet'}"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "U"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Quels sont les éléménts de l'ensemble $A$?"
      ],
      "metadata": {
        "id": "fp98VxyotDAO"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "_aNFpy9TtKXJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Afficher le type de $A$:"
      ],
      "metadata": {
        "id": "WFQqe4_F2IcI"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "J6w-P3DD2HND"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lpKjEcT700X4"
      },
      "source": [
        "## Opération sur les ensembles:\n",
        "\n",
        "  * Sous ensemble\n",
        "  * Intersection de deux ensembles\n",
        "  * Union de deux ensembles\n",
        "  * nombre d'éléments d'un ensemble"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6N9fknMb1aOT"
      },
      "source": [
        "### Sous ensemble:\n",
        "Demandons nous si $B$ est un sous ensemble de $A$, c'est à dire: $$\\Huge{B \\subset A}$$\n",
        "Le résultat est vrai (**True**) ou faux (**False**)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D6G-RPJVrPC4",
        "outputId": "3a155bbb-17d4-4cca-ca63-7627e81c89a8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "False\n",
            "True\n"
          ]
        }
      ],
      "source": [
        "print(B.issubset(A))\n",
        "print(A.issubset(U))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "acS8XtQIswWM"
      },
      "source": [
        "On utilise aussi une autre notation plus intuitive:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Am98GQoG6fDW",
        "outputId": "730bed38-b4f5-4827-c2e0-2eed5b361457"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n",
            "True\n",
            "True\n"
          ]
        }
      ],
      "source": [
        "print(U <= U)\n",
        "print(U >=U)\n",
        "print(U >= A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5-0vHgV21gO1"
      },
      "source": [
        "### Intersection de deux ensembles:\n",
        "\n",
        "On cherche des élément qui appartiennent à la fois à l'ensemble $A$ et à l'ensemble $B$. Ce qui se note mathématiquement:\n",
        "$$\\Huge{A \\cap B}$$\n",
        "En Python, on écrira de deux manières:\n",
        "\n",
        "```Python\n",
        "B.intersection(A)\n",
        "```\n",
        "ou bien:\n",
        "\n",
        "```Python\n",
        "A & B\n",
        "```\n",
        "\n",
        "Pour obtenir ces éléments"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uOFggf0arPDF"
      },
      "outputs": [],
      "source": [
        "A_inter_B = B.intersection(A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_jtW-n1IrPDO",
        "outputId": "178ce39e-5c8a-4b72-d622-5292d807f387"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'dame', 'dix'}"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "A_inter_B"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D9O2zuTBrPDc",
        "outputId": "864e54e3-49aa-4fde-9fc4-b884abaea725"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'dame', 'dix'}"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "A & B"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QMrLM6bHrPDp",
        "outputId": "60d015f1-333e-4597-a836-d523423e317b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'dame', 'dix'}"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "B & A"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aTGm6e_F1mAh"
      },
      "source": [
        "### Union de deux ensembles:\n",
        "On recherche les éléments qui appartiennent à l'ensemble $A$, à l'ensemble $B$ ou au deux, c'est à dire:\n",
        "$$\\Large{A \\cup B}$$\n",
        "En python, écrira le code suivant pour obtenir les éléments de cet ensemble:\n",
        "```Python\n",
        "A | B\n",
        "```\n",
        "ou bien encore par exemple:\n",
        "```Python\n",
        "A.union(B)\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UHLJZfmdrPD3",
        "outputId": "8b0f2372-4b34-4b11-9569-fe80d94c3928"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'as', 'dame', 'deux', 'dix', 'roi', 'sept', 'six', 'valet'}"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "A | B"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A.union(B)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H9RRxi_AtUS_",
        "outputId": "dc029773-0e43-4ca1-926b-869960833c7b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'as', 'dame', 'deux', 'dix', 'roi', 'sept', 'six', 'valet'}"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Quel autre code (utilisant la même syntaxe) permet d'obtenir $A \\cup B$?"
      ],
      "metadata": {
        "id": "crSRn-8vumCx"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "SMZzvqPzumjR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "10EbJy9a1wfk"
      },
      "source": [
        "### Nombre d'éléments d'un ensemble:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J2DQffpRrPEE",
        "outputId": "d9aaaa99-95a4-4da4-a279-cac78fa15a37"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "len(A | B)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ugV41RF627_N"
      },
      "source": [
        "# Probabilité d'un événement:\n",
        "\n",
        "   * Probabilité de l'événement $A$ : $$\\Large{P(A) = \\frac{Nombre~de~cas~favorables}\n",
        "   {Nombre~de~cas~possibles} }$$\n",
        "   * Probabilité  de l'événement $A \\cap B$ : $$\\Large{P(A \\cap B)}$$\n",
        "   * Probabilité  de l'événement $A \\cup B$ : $$\\Large{P(A \\cup B) }$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uB4p7ntprPER"
      },
      "source": [
        " **Calculons la probabilité d'un événement en python:**\n",
        "\n",
        " Avec une valeur approchée (argh!!)\n",
        "``` python\n",
        "    pA= len(A)/len(U)\n",
        "```\n",
        "maintenant avec une valeur exacte et le module *Fraction* importé plus haut:\n",
        "``` python\n",
        "    pA= Fraction(len(A),len(U))\n",
        "```\n",
        "On respire mieux. Profitons-en pour vérifier si on a bien :\n",
        "\n",
        "$$\\Large{P(A \\cup B) = P(A)+P(B)-P(A  \\cap B)}$$\n",
        "\n",
        "en montrant que:\n",
        "\n",
        "```python\n",
        "    pA_ou_B == pA+pB-pAB\n",
        "```\n",
        "est vrai"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t1eucJey4AeI",
        "outputId": "141ad6a1-a82a-433d-ee87-b61d9bd32a89"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "proba de A: 0.6363636363636364\n",
            "proba de A avec fraction: 7/11\n",
            "proba de B avec fraction: 3/11\n",
            "proba de A et B,  avec fraction: 2/11\n",
            "proba de A ou B,  avec fraction: 8/11\n"
          ]
        }
      ],
      "source": [
        "print('proba de A:', len(A)/len(U))\n",
        "pA = Fraction(len(A),len(U))\n",
        "print('proba de A avec fraction:', pA)\n",
        "pB = Fraction(len(B),len(U))\n",
        "pAB = Fraction(len(A & B),len(U))\n",
        "pA_ou_B = Fraction(len(A | B), len(U))\n",
        "print('proba de B avec fraction:', pB)\n",
        "\n",
        "print('proba de A et B,  avec fraction:', pAB)\n",
        "print('proba de A ou B,  avec fraction:', pA_ou_B)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qZADggEhrPEW",
        "outputId": "8a4b8a95-7c19-42b7-b0c8-4a9865b049f8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "pA_ou_B == pA+pB-pAB"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ENTMcLv8swWX"
      },
      "source": [
        "# Exercices"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xMz2yre7swWY"
      },
      "source": [
        "## 1-Combien  y-a-t-il d'éléments dans $\\large{C}$ ?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-69Qy3YlswWY"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9DhePtiLswWY"
      },
      "source": [
        "## 2-Quelle est la probabilité de piocher un trois, un quatre ou un cinq?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RFHqPU3iswWY"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cWY-LZHmswWY"
      },
      "source": [
        "## 3-Quelle est la probabilité de réaliser B ou C?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1jd2MUKjswWY"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GDZD_p5Q0ni1"
      },
      "source": [
        "# Représentons les ensembles avec un diagramme de Venn:\n",
        "On ne peut représenter que trois ensembles avec *venn3*."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "H5x0Ouj5r7RM",
        "outputId": "5a925427-f933-4669-bd02-e88c930ead06"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x720 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.figure(figsize=(16,10))\n",
        "\n",
        "plt.subplot(121)\n",
        "venn3([A, B, C], ('A', 'B', 'C'))\n",
        "\n",
        "plt.subplot(122)\n",
        "venn3([A, B, U], ('A', 'B', 'U'))\n",
        "\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Représentons $A\\cup B$:\n",
        "\n",
        "On constate bien que $B \\subset \\{A \\cup B\\}$"
      ],
      "metadata": {
        "id": "l7maznnExhv6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "AuB = A.union(B)\n",
        "plt.figure(figsize=(8,8))\n",
        "\n",
        "venn3([AuB, B, U], ('A u B','B', 'U'))\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "9WIehlzmxg6-",
        "outputId": "17d27300-fd7f-4428-941f-a3d7c5bbbe78"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Afficher les ensembles $A \\cap B$,  $C$ et $U$\n",
        "Vous définirez l'ensemble $A \\cap B$ par la variable **AnB**"
      ],
      "metadata": {
        "id": "rwIisSc62a1V"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "n02y7oVox5Ua"
      },
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": [
        "ejczUnhNswV5"
      ],
      "include_colab_link": true
    },
    "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": "3.7.4"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}