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231 changes: 205 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 +38,35 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"0.8844772466215439"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"from scipy.stats import binom\n",
"\n",
"n = 460\n",
"p_miss = 0.03\n",
"\n",
"prob_all_have_seats = 1 - binom.cdf(9, n, p_miss)\n",
"prob_all_have_seats"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is about an 88.45% chance that the airline will still have enough seats for all passengers."
]
},
{
Expand Down Expand Up @@ -72,11 +96,33 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 2,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"0.48999999999999994"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"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"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is a 49% chance that the representative will need 3 or more attempts to resolve the complaint."
]
},
{
Expand Down Expand Up @@ -107,11 +153,34 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"0.01289822084039205"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"from scipy.stats import poisson\n",
"\n",
"lam = 500\n",
"\n",
"prob_overwhelmed = 1 - poisson.cdf(550, lam)\n",
"prob_overwhelmed"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is about a 1.29% chance that the website server is overwhelmed in any given hour."
]
},
{
Expand All @@ -123,11 +192,30 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 4,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"0.2677043869515715"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"prob_overwhelmed_day = 1 - (1 - prob_overwhelmed)**24\n",
"prob_overwhelmed_day"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is about a 26.77% chance that the server will be overwhelmed at least once during a full day."
]
},
{
Expand Down Expand Up @@ -157,10 +245,35 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.3934693402873666"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from scipy.stats import expon\n",
"\n",
"mean_time = 10\n",
"\n",
"prob_within_5 = expon.cdf(5, scale=mean_time)\n",
"prob_within_5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"outputs": [],
"source": []
"source": [
"There is about a 39.35% chance that the next customer arrives within the next 5 minutes."
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +286,31 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.2231301601484298"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"prob_break = 1 - expon.cdf(15, scale=mean_time)\n",
"prob_break"
]
},
{
"cell_type": "markdown",
"metadata": {},
"outputs": [],
"source": []
"source": [
"There is about a 22.31% chance that no customer arrives for 15 minutes, so the employee can take a break."
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +330,35 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"0.6826894921370859"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"from scipy.stats import norm\n",
"\n",
"mu = 150\n",
"sigma = 10\n",
"\n",
"prob_between_140_160 = norm.cdf(160, loc=mu, scale=sigma) - norm.cdf(140, loc=mu, scale=sigma)\n",
"prob_between_140_160"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is about a 68.27% chance that a randomly selected bird weighs between 140g and 160g."
]
},
{
Expand All @@ -219,17 +377,38 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.4511883639059735"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_lifetime = 50\n",
"\n",
"prob_fail_30 = expon.cdf(30, scale=mean_lifetime)\n",
"prob_fail_30"
]
},
{
"cell_type": "markdown",
"metadata": {},
"outputs": [],
"source": [
"#code here"
"There is about a 45.12% chance that the component fails within the first 30 hours."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -243,7 +422,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.12.7"
}
},
"nbformat": 4,
Expand Down