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171 changes: 170 additions & 1 deletion notebook/problems.es.ipynb
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{"cells":[{"cell_type":"markdown","id":"a41f3622","metadata":{},"source":["# Ejercicios de probabilidad"]},{"cell_type":"markdown","id":"a6bdbd89","metadata":{},"source":["## Ejercicio 1 \n","\n","Dos dados se lanzan una vez y se observa el total obtenido. Usa una simulación para encontrar la probabilidad estimada de que la puntuación sea mayor a 7 o un número par. Una simulación es una repetición del mismo experimento multiples veces para observar su comportamiento:\n","\n","- Ejecuta el experimento 1000 veces (lanza 2 dados 1000 veces, y suma el número de ambos dados).\n","- Lleva ua cuenta de los números y las veces que la suma fue mayor a 7 o un número par.\n","- Divide el número del paso 2 entre el número de iteraciones(1000)."]},{"cell_type":"code","execution_count":1,"id":"8939d892","metadata":{},"outputs":[],"source":["# TODO"]},{"cell_type":"markdown","id":"55732bca","metadata":{},"source":["## Ejercicio 2\n","\n","Una caja contiene 10 bolas blancas, 20 bolas rojas y 30 bolas verdes. Si tomamos 5 bolas de la caja reemplazándolas (tomando una bola, anotando el color y luego regresandola a la caja). Queremos saber la probabilidad de:\n","\n","1. Tomar 3 blancas y 2 rojas.\n","2. Toas todas del mismo color.\n","\n","Ejecuta el experimento 1000 veces y calcula las probabilidades que mencionadas."]},{"cell_type":"code","execution_count":null,"id":"23244d20","metadata":{},"outputs":[{"ename":"","evalue":"","output_type":"error","traceback":["\u001b[1;31mRunning cells with 'c:\\Program Files\\Python312\\python.exe' requires the ipykernel package.\n","\u001b[1;31mRun the following command to install 'ipykernel' into the Python environment. \n","\u001b[1;31mCommand: '\"c:/Program Files/Python312/python.exe\" -m pip install ipykernel -U --user --force-reinstall'"]}],"source":["ball_box = {}\n","\n","# Crea la cajas con las bolas\n","for i in range(60):\n"," if i < 10:\n"," ball_box[i] = \"White\"\n"," elif (i > 9) and (i < 30):\n"," ball_box[i] = \"Red\"\n"," else:\n"," ball_box[i] = \"Green\"\n","\n","print(ball_box)\n"," \n","# TODO"]}],"metadata":{"interpreter":{"hash":"9248718ffe6ce6938b217e69dbcc175ea21f4c6b28a317e96c05334edae734bb"},"kernelspec":{"display_name":"Python 3.9.12 ('ML-BOOTCAMP')","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":"3.12.1"}},"nbformat":4,"nbformat_minor":5}
{
"cells": [
{
"cell_type": "markdown",
"id": "a41f3622",
"metadata": {},
"source": [
"# Ejercicios de probabilidad"
]
},
{
"cell_type": "markdown",
"id": "a6bdbd89",
"metadata": {},
"source": [
"## Ejercicio 1 \n",
"\n",
"Dos dados se lanzan una vez y se observa el total obtenido. Usa una simulación para encontrar la probabilidad estimada de que la puntuación sea mayor a 7 o un número par. Una simulación es una repetición del mismo experimento multiples veces para observar su comportamiento:\n",
"\n",
"- Ejecuta el experimento 1000 veces (lanza 2 dados 1000 veces, y suma el número de ambos dados).\n",
"- Lleva ua cuenta de los números y las veces que la suma fue mayor a 7 o un número par.\n",
"- Divide el número del paso 2 entre el número de iteraciones(1000)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "8939d892",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability of rolling an even number or greater than 7 is: 67.9%\n"
]
}
],
"source": [
"# TODO\n",
"\n",
"import random\n",
"import numpy as np\n",
"\n",
"def roll_the_dice(n_simulations = 1000):\n",
" count = 0\n",
" \n",
" # Each iteration of the for loop is a trial\n",
" for i in range(n_simulations):\n",
" \n",
" # Roll each dice\n",
" die1 = random.randint(1, 6)\n",
" die2 = random.randint(1, 6)\n",
" \n",
" # Sum the values to get the score\n",
" score = die1 + die2\n",
" \n",
" # Decide if we should add it to the count:\n",
" if (score % 2 == 0) or (score > 7):\n",
" count += 1\n",
"\n",
" # Calculate probability\n",
" return count / n_simulations\n",
"\n",
"print(f\"The probability of rolling an even number or greater than 7 is: {np.round(roll_the_dice() * 100, 2)}%\")"
]
},
{
"cell_type": "markdown",
"id": "55732bca",
"metadata": {},
"source": [
"## Ejercicio 2\n",
"\n",
"Una caja contiene 10 bolas blancas, 20 bolas rojas y 30 bolas verdes. Si tomamos 5 bolas de la caja reemplazándolas (tomando una bola, anotando el color y luego regresandola a la caja). Queremos saber la probabilidad de:\n",
"\n",
"1. Tomar 3 blancas y 2 rojas.\n",
"2. Toas todas del mismo color.\n",
"\n",
"Ejecuta el experimento 1000 veces y calcula las probabilidades que mencionadas."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "23244d20",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{0: 'White', 1: 'White', 2: 'White', 3: 'White', 4: 'White', 5: 'White', 6: 'White', 7: 'White', 8: 'White', 9: 'White', 10: 'Red', 11: 'Red', 12: 'Red', 13: 'Red', 14: 'Red', 15: 'Red', 16: 'Red', 17: 'Red', 18: 'Red', 19: 'Red', 20: 'Red', 21: 'Red', 22: 'Red', 23: 'Red', 24: 'Red', 25: 'Red', 26: 'Red', 27: 'Red', 28: 'Red', 29: 'Red', 30: 'Green', 31: 'Green', 32: 'Green', 33: 'Green', 34: 'Green', 35: 'Green', 36: 'Green', 37: 'Green', 38: 'Green', 39: 'Green', 40: 'Green', 41: 'Green', 42: 'Green', 43: 'Green', 44: 'Green', 45: 'Green', 46: 'Green', 47: 'Green', 48: 'Green', 49: 'Green', 50: 'Green', 51: 'Green', 52: 'Green', 53: 'Green', 54: 'Green', 55: 'Green', 56: 'Green', 57: 'Green', 58: 'Green', 59: 'Green'}\n",
"The probability of 3 white and 2 red is: 0.3%\n",
"The probability of all the same color is: 3.5%\n"
]
}
],
"source": [
"ball_box = {}\n",
"\n",
"# Crea la cajas con las bolas\n",
"for i in range(60):\n",
" if i < 10:\n",
" ball_box[i] = \"White\"\n",
" elif (i > 9) and (i < 30):\n",
" ball_box[i] = \"Red\"\n",
" else:\n",
" ball_box[i] = \"Green\"\n",
"\n",
"print(ball_box)\n",
" \n",
"# TODO\n",
"\n",
"def take_balls(n_simulations = 1000):\n",
" count_1 = 0\n",
" count_2 = 0\n",
"\n",
" for i in range(n_simulations):\n",
" colors = []\n",
"\n",
" # Take 5 balls from the box\n",
" for i in range(5):\n",
" colors.append(ball_box[np.random.randint(0, 59)])\n",
"\n",
" # Convert list to Numpy array for better filtering\n",
" colors = np.array(colors)\n",
" \n",
" white_balls = sum(colors == \"White\")\n",
" red_balls = sum(colors == \"Red\")\n",
" green_balls = sum(colors == \"Green\")\n",
"\n",
" # Decide if we should add it to the count:\n",
" if (white_balls == 3) and (red_balls == 2):\n",
" count_1 += 1\n",
" \n",
" if (white_balls == 5) or (red_balls == 5) or (green_balls == 5):\n",
" count_2 += 1\n",
" \n",
" return count_1 / n_simulations, count_2 / n_simulations\n",
"\n",
"probabilities = take_balls(1000)\n",
"\n",
"print(f\"The probability of 3 white and 2 red is: {np.round(probabilities[0] * 100, 2)}%\")\n",
"print(f\"The probability of all the same color is: {np.round(probabilities[1] * 100, 2)}%\")"
]
}
],
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"kernelspec": {
"display_name": "Python 3",
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},
"language_info": {
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"file_extension": ".py",
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