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Completed intro to probability lab #470

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180 changes: 154 additions & 26 deletions lab-intro-probability.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -38,11 +38,29 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability that all passengers get a seat: 0.8845\n",
"Percentage: 88.45%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import binom\n",
"\n",
"n = 460 \n",
"p_miss = 0.03 \n",
"seats = 450\n",
"\n",
"prob_seats_for_all = 1 - binom.cdf(9, n, p_miss)\n",
"\n",
"print(f\"Probability that all passengers get a seat: {prob_seats_for_all:.4f}\")\n",
"print(f\"Percentage: {prob_seats_for_all*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -72,11 +90,25 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 2,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability that at least 3 attempts are needed: 0.4900\n",
"Percentage: 49.00%\n"
]
}
],
"source": [
"#code here"
"p_success = 0.3\n",
"\n",
"prob_at_least_3_attempts = (1 - p_success) ** 2\n",
"\n",
"print(f\"Probability that at least 3 attempts are needed: {prob_at_least_3_attempts:.4f}\")\n",
"print(f\"Percentage: {prob_at_least_3_attempts*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -107,11 +139,28 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability the server is overwhelmed in one hour: 0.0129\n",
"Percentage: 1.29%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import poisson\n",
"\n",
"lam = 500 \n",
"capacity = 550\n",
"\n",
"prob_overwhelmed_hour = 1 - poisson.cdf(capacity, lam)\n",
"\n",
"print(f\"Probability the server is overwhelmed in one hour: {prob_overwhelmed_hour:.4f}\")\n",
"print(f\"Percentage: {prob_overwhelmed_hour*100:.2f}%\")"
]
},
{
Expand All @@ -123,11 +172,25 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 4,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability the server is overwhelmed at least once in 24 hours: 0.2677\n",
"Percentage: 26.77%\n"
]
}
],
"source": [
"#code here"
"prob_not_overwhelmed_hour = 1 - prob_overwhelmed_hour\n",
"\n",
"prob_overwhelmed_day = 1 - (prob_not_overwhelmed_hour ** 24)\n",
"\n",
"print(f\"Probability the server is overwhelmed at least once in 24 hours: {prob_overwhelmed_day:.4f}\")\n",
"print(f\"Percentage: {prob_overwhelmed_day*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -157,10 +220,29 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability the next customer arrives within 5 minutes: 0.3935\n",
"Percentage: 39.35%\n"
]
}
],
"source": [
"import numpy as np\n",
"\n",
"mean_time = 10 \n",
"rate = 1 / mean_time\n",
"\n",
"prob_within_5 = 1 - np.exp(-rate * 5)\n",
"\n",
"print(f\"Probability the next customer arrives within 5 minutes: {prob_within_5:.4f}\")\n",
"print(f\"Percentage: {prob_within_5*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +255,24 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability an employee can take a break: 0.2231\n",
"Percentage: 22.31%\n"
]
}
],
"source": [
"prob_break = np.exp(-rate * 15)\n",
"\n",
"print(f\"Probability an employee can take a break: {prob_break:.4f}\")\n",
"print(f\"Percentage: {prob_break*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +292,28 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability the bird weighs between 140g and 160g: 0.6827\n",
"Percentage: 68.27%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import norm\n",
"\n",
"mu = 150\n",
"sigma = 10\n",
"\n",
"prob_between = norm.cdf(160, mu, sigma) - norm.cdf(140, mu, sigma)\n",
"\n",
"print(f\"Probability the bird weighs between 140g and 160g: {prob_between:.4f}\")\n",
"print(f\"Percentage: {prob_between*100:.2f}%\")"
]
},
{
Expand All @@ -219,17 +332,32 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 8,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability the component fails within the first 30 hours: 0.4512\n",
"Percentage: 45.12%\n"
]
}
],
"source": [
"#code here"
"mean_lifetime = 50 \n",
"rate = 1 / mean_lifetime\n",
"\n",
"prob_fail_30 = 1 - np.exp(-rate * 30)\n",
"\n",
"print(f\"Probability the component fails within the first 30 hours: {prob_fail_30:.4f}\")\n",
"print(f\"Percentage: {prob_fail_30*100:.2f}%\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -243,7 +371,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.5"
}
},
"nbformat": 4,
Expand Down