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219 changes: 195 additions & 24 deletions lab-intro-probability.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -40,9 +40,34 @@
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Challenge 1: Ironhack Airlines\n",
"Probability all passengers have seats: 0.8845\n",
"That's about 88.45%\n"
]
}
],
"source": [
"#code here"
"# Challenge ones\n",
"\n",
"from scipy.stats import binom\n",
"import numpy as np\n",
"\n",
"# plane has 450 seats, sells 460 tickets\n",
"# Each passenger has 3% chance of missing (97% show up)\n",
"n = 460 # tickets sold\n",
"p = 0.97 # probability of showing up\n",
"\n",
"# we want probability that 450 or fewer show up\n",
"prob_all_seated = binom.cdf(450, n, p)\n",
"\n",
"print(f\"Challenge 1: Ironhack Airlines\")\n",
"print(f\"Probability all passengers have seats: {prob_all_seated:.4f}\")\n",
"print(f\"That's about {prob_all_seated*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -72,11 +97,36 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 2,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Challenge 2: Call Center\n",
"Probability needs at least 3 attempts: 0.4900\n",
"Or about 49.00%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import geom\n",
"\n",
"# probability of success on first attempt = 0.3\n",
"p = 0.3\n",
"\n",
"# need at least 3 attempts means first 2 fail\n",
"# P(X >= 3) = 1 - P(X < 3) = 1 - P(X=1) - P(X=2)\n",
"\n",
"prob_1 = geom.pmf(1, p)\n",
"prob_2 = geom.pmf(2, p)\n",
"\n",
"prob_at_least_3 = 1 - prob_1 - prob_2\n",
"\n",
"print(\"Challenge 2: Call Center\")\n",
"print(f\"Probability needs at least 3 attempts: {prob_at_least_3:.4f}\")\n",
"print(f\"Or about {prob_at_least_3*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -107,11 +157,30 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Challenge 3: Website\n",
"Probability server overwhelmed in 1 hour: 0.0129\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import poisson\n",
"\n",
"# average 500 visits per hour\n",
"# server handles up to 550\n",
"lambda_rate = 500\n",
"\n",
"# probability of MORE than 550 visits\n",
"prob_overwhelmed = 1 - poisson.cdf(550, lambda_rate)\n",
"\n",
"print(\"Challenge 3: Website\")\n",
"print(f\"Probability server overwhelmed in 1 hour: {prob_overwhelmed:.4f}\")#code here"
]
},
{
Expand All @@ -123,11 +192,30 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of being overwhelmed during the 24 hours: 0.2677\n",
"result is 26.77%\n"
]
}
],
"source": [
"#code here"
"# whats probability not overwhelmed in one hour\n",
"prob_not_overwhelmed = 1 - prob_overwhelmed\n",
"\n",
"# probability of being not overwhelmed for all 24 hours\n",
"prob_never_overwhelmed_24h = prob_not_overwhelmed ** 24\n",
"\n",
"# probability overwhelmed at least once\n",
"prob_overwhelmed_24h = 1 - prob_never_overwhelmed_24h\n",
"\n",
"print(f\"Probability of being overwhelmed during the 24 hours: {prob_overwhelmed_24h:.4f}\")\n",
"print(f\"result is {prob_overwhelmed_24h*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -159,8 +247,32 @@
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Challenge 4: Helpdesk\n",
"Probability customer arrives within 5 min: 0.3935\n",
"roughly 39.3%\n"
]
}
],
"source": [
"from scipy.stats import expon\n",
"\n",
"# average customer every ten mins\n",
"# so lambda = 1/10 = 0.1 per minute\n",
"mean_time = 10\n",
"lambda_rate = 1/mean_time\n",
"\n",
"# probability next customer arrives within 5 minutes\n",
"prob_within_5 = expon.cdf(5, scale=mean_time)\n",
"\n",
"print(\"Challenge 4: Helpdesk\")\n",
"print(f\"Probability customer arrives within 5 min: {prob_within_5:.4f}\")\n",
"print(f\"roughly {prob_within_5*100:.1f}%\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +285,28 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Probability employee gets a break: 0.2231\n",
"Result is 22.31%\n"
]
}
],
"source": [
"# probability no customer for 15 minutes (employee gets break)\n",
"\n",
"# this is P(X > 15)\n",
"prob_no_customer_15 = 1 - expon.cdf(15, scale=mean_time)\n",
"\n",
"print(f\"\\nProbability employee gets a break: {prob_no_customer_15:.4f}\")\n",
"print(f\"Result is {prob_no_customer_15*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +326,32 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 14,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Challenge 5: Bird Weights\n",
"Probability weight is between 140-160g: 0.6827\n",
"Final result is 68.27%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import norm\n",
"\n",
"# mean is 150g, std dev is 10g\n",
"mean = 150\n",
"std = 10\n",
"\n",
"# probability of between 140 and 160\n",
"prob_between = norm.cdf(160, mean, std) - norm.cdf(140, mean, std)\n",
"\n",
"print(\"Challenge 5: Bird Weights\")\n",
"print(f\"Probability weight is between 140-160g: {prob_between:.4f}\")\n",
"print(f\"Final result is {prob_between*100:.2f}%\")"
]
},
{
Expand All @@ -219,17 +370,37 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 15,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Challenge 6: Electronic Component\n",
"Probability component fails within 30 hours: 0.4512\n",
"About 45.1%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import expon\n",
"\n",
"# mean lifetime is 50 hours\n",
"mean_lifetime = 50\n",
"\n",
"# probability of it fails within first 30 hours\n",
"prob_fail_30 = expon.cdf(30, scale=mean_lifetime)\n",
"\n",
"print(\"Challenge 6: Electronic Component\")\n",
"print(f\"Probability component fails within 30 hours: {prob_fail_30:.4f}\")\n",
"print(f\"About {prob_fail_30*100:.1f}%\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -243,7 +414,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.5"
}
},
"nbformat": 4,
Expand Down