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ejercicios de probabilidad #13

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2 changes: 1 addition & 1 deletion notebook/problems.ipynb
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{"cells":[{"cell_type":"markdown","id":"a41f3622","metadata":{},"source":["# Probability exercises"]},{"cell_type":"markdown","id":"a6bdbd89","metadata":{},"source":["## Exercise 1 \n","\n","Two dices are thrown once and the total score is observed. Use a simulation to find the estimated probability that the total score is even or greater than 7. A simulation is a repetition of the same experiment multiple times to observe its behavior:\n","\n","- Run the experiment 1000 times (roll 2 dice 1000 times, and sum the number of both dices).\n","- Keep track of the number of times that the sum was either greater than 7 or an even number.\n","- Divide the number from step 2 by the number of iterations (1000)."]},{"cell_type":"code","execution_count":1,"id":"8939d892","metadata":{},"outputs":[],"source":["# TODO"]},{"cell_type":"markdown","id":"55732bca","metadata":{},"source":["## Exercise 2\n","\n","A box contains 10 white balls, 20 red balls and 30 green balls. If we take 5 balls from the box with replacement (we take the ball, observe what color it is and put it back into the box). We want to know the probability of:\n","\n","1. Take 3 white and 2 red.\n","2. All are the same color.\n","\n","Run the experiment 1000 times and calculate the above probabilities."]},{"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"]}],"source":["ball_box = {}\n","\n","# Create the box of balls\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":"3.11.4"}},"nbformat":4,"nbformat_minor":5}
{"cells":[{"cell_type":"markdown","id":"a41f3622","metadata":{},"source":["# Probability exercises"]},{"cell_type":"markdown","id":"a6bdbd89","metadata":{},"source":["## Exercise 1 \n","\n","Two dices are thrown once and the total score is observed. Use a simulation to find the estimated probability that the total score is even or greater than 7. A simulation is a repetition of the same experiment multiple times to observe its behavior:\n","\n","- Run the experiment 1000 times (roll 2 dice 1000 times, and sum the number of both dices).\n","- Keep track of the number of times that the sum was either greater than 7 or an even number.\n","- Divide the number from step 2 by the number of iterations (1000)."]},{"cell_type":"code","execution_count":9,"id":"8939d892","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["La porbabilidad de tirar el dado y que salga un numero par o mayor que 7 es: {68.2} %\n"]}],"source":["# TODO\n","import random\n","import numpy as np\n","def tirar_el_dado(n_simulaciones = 1000):\n"," count = 0\n","\n"," for i in range(n_simulaciones):\n"," dado1= random.randint(1,6)\n"," dado2= random.randint(1,6)\n"," resultado = dado1 + dado2\n","\n"," if (resultado % 2 ==0) or (resultado > 7):\n"," count += 1\n","\n"," return count / n_simulaciones\n","\n","print(f\"La porbabilidad de tirar el dado y que salga un numero par o mayor que 7 es:\" , {np.round(tirar_el_dado() * 100 , 2)} , \"%\")\n","\n"]},{"cell_type":"markdown","id":"55732bca","metadata":{},"source":["## Exercise 2\n","\n","A box contains 10 white balls, 20 red balls and 30 green balls. If we take 5 balls from the box with replacement (we take the ball, observe what color it is and put it back into the box). We want to know the probability of:\n","\n","1. Take 3 white and 2 red.\n","2. All are the same color.\n","\n","Run the experiment 1000 times and calculate the above probabilities."]},{"cell_type":"code","execution_count":20,"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","La probabilidad que salgan 3 blancas y 2 rojas es: 0.8%\n","La probabilidad que salgan todas del mismo color es: 2.8%\n"]}],"source":["import numpy as np\n","\n","ball_box = {}\n","\n","# Create the box of balls\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 tomar_bolas (n_experimentos = 1000):\n"," cuenta_1 = 0\n"," cuenta_2 = 0\n"," for i in range(n_experimentos):\n"," colors = []\n","\n"," for i in range (5):\n"," colors.append(ball_box[np.random.randint(0, 59)])\n"," colors = np.array(colors) \n","\n"," bolas_blancas = sum(colors == \"White\")\n"," bolas_verdes = sum(colors == \"Green\")\n"," bolas_rojas = sum(colors == \"Red\")\n","\n"," if (bolas_blancas == 3) and (bolas_rojas == 2):\n"," cuenta_1 += 1 \n"," if (bolas_blancas == 5) or (bolas_rojas == 5) or (bolas_verdes == 5):\n"," cuenta_2 += 1\n","\n"," return cuenta_1 / n_experimentos , cuenta_2 / n_experimentos\n","\n","probabilidad = tomar_bolas(1000)\n","\n","print(f\"La probabilidad que salgan 3 blancas y 2 rojas es: {np.round(probabilidad[0] * 100, 2)}%\")\n","print(f\"La probabilidad que salgan todas del mismo color es: {np.round(probabilidad[1] * 100, 2)}%\")\n"]}],"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":"3.11.4"}},"nbformat":4,"nbformat_minor":5}
2 changes: 1 addition & 1 deletion notebook/solutions.ipynb
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{"cells":[{"cell_type":"markdown","id":"a41f3622","metadata":{},"source":["# Solutions"]},{"cell_type":"markdown","id":"a6bdbd89","metadata":{},"source":["## Exercise 1 "]},{"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: 66.8%\n"]}],"source":["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":["## Exercise 2"]},{"cell_type":"code","execution_count":2,"id":"d9b7e024","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: 0.4%\n","The probability of all the same color is: 3.2%\n"]}],"source":["ball_box = {}\n","\n","# Create the box of balls\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","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)}%\")"]}],"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":"3.11.4"}},"nbformat":4,"nbformat_minor":5}
{"cells":[{"cell_type":"markdown","id":"a41f3622","metadata":{},"source":["# Solutions"]},{"cell_type":"markdown","id":"a6bdbd89","metadata":{},"source":["## Exercise 1 "]},{"cell_type":"code","execution_count":5,"id":"8939d892","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["The probability of rolling an even number or greater than 7 is: 68.9%\n"]}],"source":["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":["## Exercise 2"]},{"cell_type":"code","execution_count":2,"id":"d9b7e024","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"]},{"ename":"NameError","evalue":"name 'np' is not defined","output_type":"error","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)","\u001b[1;32m/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb Celda 5\u001b[0m line \u001b[0;36m4\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=36'>37</a>\u001b[0m count_2 \u001b[39m+\u001b[39m\u001b[39m=\u001b[39m \u001b[39m1\u001b[39m\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=38'>39</a>\u001b[0m \u001b[39mreturn\u001b[39;00m count_1 \u001b[39m/\u001b[39m n_simulations, count_2 \u001b[39m/\u001b[39m n_simulations\n\u001b[0;32m---> <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=40'>41</a>\u001b[0m probabilities \u001b[39m=\u001b[39m take_balls(\u001b[39m1000\u001b[39;49m)\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=42'>43</a>\u001b[0m \u001b[39mprint\u001b[39m(\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mThe probability of 3 white and 2 red is: \u001b[39m\u001b[39m{\u001b[39;00mnp\u001b[39m.\u001b[39mround(probabilities[\u001b[39m0\u001b[39m]\u001b[39m \u001b[39m\u001b[39m*\u001b[39m\u001b[39m \u001b[39m\u001b[39m100\u001b[39m,\u001b[39m \u001b[39m\u001b[39m2\u001b[39m)\u001b[39m}\u001b[39;00m\u001b[39m%\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=43'>44</a>\u001b[0m \u001b[39mprint\u001b[39m(\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mThe probability of all the same color is: \u001b[39m\u001b[39m{\u001b[39;00mnp\u001b[39m.\u001b[39mround(probabilities[\u001b[39m1\u001b[39m]\u001b[39m \u001b[39m\u001b[39m*\u001b[39m\u001b[39m \u001b[39m\u001b[39m100\u001b[39m,\u001b[39m \u001b[39m\u001b[39m2\u001b[39m)\u001b[39m}\u001b[39;00m\u001b[39m%\u001b[39m\u001b[39m\"\u001b[39m)\n","\u001b[1;32m/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb Celda 5\u001b[0m line \u001b[0;36m2\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=20'>21</a>\u001b[0m \u001b[39m# Take 5 balls from the box\u001b[39;00m\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=21'>22</a>\u001b[0m \u001b[39mfor\u001b[39;00m i \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(\u001b[39m5\u001b[39m):\n\u001b[0;32m---> <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=22'>23</a>\u001b[0m colors\u001b[39m.\u001b[39mappend(ball_box[np\u001b[39m.\u001b[39mrandom\u001b[39m.\u001b[39mrandint(\u001b[39m0\u001b[39m, \u001b[39m59\u001b[39m)])\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=24'>25</a>\u001b[0m \u001b[39m# Convert list to Numpy array for better filtering\u001b[39;00m\n\u001b[1;32m <a href='vscode-notebook-cell://codespaces%2Bliterate-space-guide-69g4vrq54xg6h4vgg/workspaces/probability-exercises-project-in-python/notebook/solutions.ipynb#W4sdnNjb2RlLXJlbW90ZQ%3D%3D?line=25'>26</a>\u001b[0m colors \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marray(colors)\n","\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"]}],"source":["ball_box = {}\n","\n","# Create the box of balls\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","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)}%\")"]}],"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":"3.11.4"}},"nbformat":4,"nbformat_minor":5}