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216 changes: 190 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 +38,36 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Challenge 1\n",
"Probability there are seats for all passengers: 0.884477\n"
]
}
],
"source": [
"#code here"
"import math\n",
"from scipy.stats import binom, geom, poisson, expon, norm\n",
"\n",
"# Challenge 1\n",
"# Ironhack Airlines\n",
"# Seats available for all passengers means at most 450 passengers show up.\n",
"# If 460 tickets are sold and each passenger misses with probability 0.03,\n",
"# then each passenger shows up with probability 0.97.\n",
"\n",
"n_tickets = 460\n",
"p_show = 0.97\n",
"seats = 450\n",
"\n",
"prob_seats_for_all = binom.cdf(seats, n_tickets, p_show)\n",
"\n",
"print(\"Challenge 1\")\n",
"print(f\"Probability there are seats for all passengers: {prob_seats_for_all:.6f}\")"
]
},
{
Expand Down Expand Up @@ -72,11 +97,31 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Challenge 2\n",
"Probability of needing at least 3 attempts: 0.490000\n"
]
}
],
"source": [
"#code here"
"# Ironhack Call Center\n",
"# Success on first attempt probability = 0.3\n",
"# Need at least 3 attempts before success means:\n",
"# first two attempts fail.\n",
"# Probability = (1 - 0.3)^2\n",
"\n",
"p_success = 0.3\n",
"prob_at_least_3_attempts = (1 - p_success) ** 2\n",
"\n",
"print(\"\\nChallenge 2\")\n",
"print(f\"Probability of needing at least 3 attempts: {prob_at_least_3_attempts:.6f}\")\n"
]
},
{
Expand Down Expand Up @@ -107,11 +152,31 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 4,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Challenge 3\n",
"Probability server is overwhelmed in one hour: 0.012898\n"
]
}
],
"source": [
"#code here"
"# Ironhack Website\n",
"# Visits per hour follow a Poisson distribution with lambda = 500.\n",
"# Server is overwhelmed if visits exceed 550 in one hour.\n",
"\n",
"lam_hour = 500\n",
"capacity = 550\n",
"\n",
"prob_overwhelmed_one_hour = 1 - poisson.cdf(capacity, lam_hour)\n",
"\n",
"print(\"\\nChallenge 3\")\n",
"print(f\"Probability server is overwhelmed in one hour: {prob_overwhelmed_one_hour:.6f}\")"
]
},
{
Expand All @@ -123,11 +188,23 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 5,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability server is overwhelmed at least once during the day: 0.267704\n"
]
}
],
"source": [
"#code here"
"# 1 - P(not overwhelmed in any hour)^24\n",
"\n",
"prob_overwhelmed_some_point_day = 1 - (1 - prob_overwhelmed_one_hour) ** 24\n",
"\n",
"print(f\"Probability server is overwhelmed at least once during the day: {prob_overwhelmed_some_point_day:.6f}\")\n"
]
},
{
Expand Down Expand Up @@ -157,10 +234,38 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Challenge 4\n",
"Probability next customer arrives within 5 minutes: 0.393469\n",
"Probability an employee can take a break: 0.223130\n"
]
}
],
"source": [
"# Arrivals follow an exponential distribution.\n",
"# Average arrival every 10 minutes means rate lambda = 1/10 per minute.\n",
"\n",
"mean_minutes = 10\n",
"rate = 1 / mean_minutes\n",
"\n",
"# Probability next customer arrives within 5 minutes\n",
"prob_within_5 = expon.cdf(5, scale=mean_minutes)\n",
"\n",
"# Probability no customer arrives for 15 minutes\n",
"# If no customer for 15 minutes, employee can take a break\n",
"prob_break = 1 - expon.cdf(15, scale=mean_minutes)\n",
"\n",
"print(\"\\nChallenge 4\")\n",
"print(f\"Probability next customer arrives within 5 minutes: {prob_within_5:.6f}\")\n",
"print(f\"Probability an employee can take a break: {prob_break:.6f}\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +278,32 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Challenge 4\n",
"Probability next customer arrives within 5 minutes: 0.393469\n",
"Probability an employee can take a break: 0.223130\n"
]
}
],
"source": [
"# Probability next customer arrives within 5 minutes\n",
"prob_within_5 = expon.cdf(5, scale=mean_minutes)\n",
"\n",
"# Probability no customer arrives for 15 minutes\n",
"# If no customer for 15 minutes, employee can take a break\n",
"prob_break = 1 - expon.cdf(15, scale=mean_minutes)\n",
"\n",
"print(\"\\nChallenge 4\")\n",
"print(f\"Probability next customer arrives within 5 minutes: {prob_within_5:.6f}\")\n",
"print(f\"Probability an employee can take a break: {prob_break:.6f}\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +323,27 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 8,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Challenge 5\n",
"Probability bird weighs between 140g and 160g: 0.682689\n"
]
}
],
"source": [
"#code here"
"mu = 150\n",
"sigma = 10\n",
"\n",
"prob_between_140_160 = norm.cdf(160, mu, sigma) - norm.cdf(140, mu, sigma)\n",
"\n",
"print(\"\\nChallenge 5\")\n",
"print(f\"Probability bird weighs between 140g and 160g: {prob_between_140_160:.6f}\")\n"
]
},
{
Expand All @@ -219,17 +362,38 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 9,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Challenge 6\n",
"Probability component fails within first 30 hours: 0.451188\n"
]
}
],
"source": [
"#code here"
"mean_lifetime = 50\n",
"prob_fail_30 = expon.cdf(30, scale=mean_lifetime)\n",
"\n",
"print(\"\\nChallenge 6\")\n",
"print(f\"Probability component fails within first 30 hours: {prob_fail_30:.6f}\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -243,7 +407,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.9"
}
},
"nbformat": 4,
Expand Down