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# Update lab-intro-probability.ipynb #481

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# Update lab-intro-probability.ipynb #481

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174 changes: 148 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": 2,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that all 10 passengers will have seats is: 0.8845\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"\n",
"from scipy.stats import binom\n",
"\n",
"n = 460\n",
"p_miss = 0.03\n",
"\n",
"prob_seats_for_all = 1 - binom.cdf(9, n, p_miss)\n",
"prob_seats_for_all\n",
"\n",
"print(f\"The probability that all 10 passengers will have seats is: {prob_seats_for_all:.4f}\") \n"
]
},
{
Expand Down Expand Up @@ -72,11 +90,27 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that the first success occurs on the third attempt or later is: 0.4900\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"\n",
"p_success = 0.3\n",
"p_fail = 1 - p_success\n",
"\n",
"prob_at_least_3_attempts = p_fail ** 2\n",
"prob_at_least_3_attempts\n",
"\n",
"print(f\"The probability that the first success occurs on the third attempt or later is: {prob_at_least_3_attempts:.4f}\") \n"
]
},
{
Expand Down Expand Up @@ -107,11 +141,25 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that the hospital will be overwhelmed in a given hour is: 0.0129\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"\n",
"lam = 500\n",
"\n",
"prob_overwhelmed_hour = poisson.sf(550, lam) # P(X > 550)\n",
"prob_overwhelmed_hour\n",
"print(f\"The probability that the hospital will be overwhelmed in a given hour is: {prob_overwhelmed_hour:.4f}\")\n"
]
},
{
Expand All @@ -123,11 +171,24 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 5,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that the hospital will be overwhelmed at least once in a day is: 0.2677\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"\n",
"prob_overwhelmed_day = 1 - (1 - prob_overwhelmed_hour) ** 24\n",
"prob_overwhelmed_day\n",
"\n",
"print(f\"The probability that the hospital will be overwhelmed at least once in a day is: {prob_overwhelmed_day:.4f}\") \n"
]
},
{
Expand Down Expand Up @@ -157,10 +218,26 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that the next arrival occurs within 5 minutes is: 0.3935\n"
]
}
],
"source": [
"lambda_rate = 1/10 # arrivals per minute\n",
"\n",
"# P(X <= 5)\n",
"prob_within_5 = expon.cdf(5, scale=1/lambda_rate)\n",
"prob_within_5\n",
"\n",
"print(f\"The probability that the next arrival occurs within 5 minutes is: {prob_within_5:.4f}\")\n"
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +250,24 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that no customer arrives in the next 15 minutes is: 0.2231\n"
]
}
],
"source": [
"# P(X > 15)\n",
"prob_no_customer_15 = expon.sf(15, scale=1/lambda_rate)\n",
"prob_no_customer_15\n",
"\n",
"print(f\"The probability that no customer arrives in the next 15 minutes is: {prob_no_customer_15:.4f}\") \n"
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +287,27 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 15,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that the weight of a randomly selected package is between 140 and 160 grams is: 0.6827\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"from scipy.stats import norm\n",
"mean = 150\n",
"std = 10\n",
"\n",
"prob_between = norm.cdf(160, loc=mean, scale=std) - norm.cdf(140, loc=mean, scale=std)\n",
"prob_between\n",
"\n",
"print(f\"The probability that the weight of a randomly selected package is between 140 and 160 grams is: {prob_between:.4f}\")"
]
},
{
Expand All @@ -219,17 +326,32 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 16,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that the machine fails within 30 minutes is: 0.4512\n"
]
}
],
"source": [
"#code here"
"#code here\n",
"\n",
"lambda_rate = 1/50\n",
"\n",
"prob_fail_30 = expon.cdf(30, scale=1/lambda_rate)\n",
"prob_fail_30\n",
"\n",
"print(f\"The probability that the machine fails within 30 minutes is: {prob_fail_30:.4f}\") "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -243,7 +365,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.5"
}
},
"nbformat": 4,
Expand Down