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lab solved #473

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245 changes: 221 additions & 24 deletions lab-intro-probability.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -36,13 +36,39 @@
"If the Ironhack Airlines routinely sells 460 tickets, what is the chance that they have a seats for all passenger?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Binominal challenge"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability that all passengers get a seat: 0.8845\n",
"That's about 88.45%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import binom\n",
"#tickets sold\n",
"n = 460\n",
"#chance of catching the flight\n",
"p = 0.97\n",
"seats = 450\n",
"#P( or fewer passengers show up)\n",
"probability = binom.cdf(seats, n, p)\n",
"\n",
"print(f\"Probability that all passengers get a seat: {probability:.4f}\")\n",
"print(f\"That's about {probability*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -70,13 +96,56 @@
"What is the probability that the representative needs to make at least three attempts before successfully resolving a customer complaint?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Geometric distribution problem"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of needing at least 3 attempts: 0.4900\n",
"That's about 49.00%\n"
]
}
],
"source": [
"from scipy.stats import geom\n",
"# Parameters\n",
"p = 0.3 # probability of resolving on first attempt\n",
"\n",
"# P(needs AT LEAST 3 attempts) = P(first success happens on attempt 3 or later)\n",
"probability = geom.sf(2, p) # sf(2) means \"more than 2 attempts\", sf= survival function\n",
"\n",
"print(f\"Probability of needing at least 3 attempts: {probability:.4f}\")\n",
"print(f\"That's about {probability*100:.2f}%\")"
]
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of resolving within 2 attempts: 51.00%\n"
]
}
],
"source": [
"#code here"
"# P(resolves on attempt 1 or 2)\n",
"probability_1_or_2 = geom.cdf(2, p) #cdf = Cumulative distribution function, For dummies: \"What is the probability of getting X or LESS?\"\n",
"print(f\"Probability of resolving within 2 attempts: {probability_1_or_2*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -105,13 +174,38 @@
"What is the probability of the website server being overwhelmed?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Poisson distribution"
]
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of server being overwhelmed: 0.0129\n",
"That's about 1.29%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import poisson\n",
"# Parameters\n",
"mu = 500 # average visits per hour #mu is greek letter for M (weird u)\n",
"capacity = 550 # server capacity\n",
"\n",
"# P(more than 550 visits) = server overwhelmed\n",
"probability = poisson.sf(capacity, mu)\n",
"\n",
"print(f\"Probability of server being overwhelmed: {probability:.4f}\")\n",
"print(f\"That's about {probability*100:.2f}%\")"
]
},
{
Expand All @@ -123,11 +217,30 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 8,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of being overwhelmed at least once in 24 hours: 0.2677\n",
"That's about 26.77%\n"
]
}
],
"source": [
"#code here"
"# Probability of NOT being overwhelmed in a single hour\n",
"p_safe_one_hour = 1 - probability # from previous result\n",
"\n",
"# Probability of NOT being overwhelmed in ALL 24 hours\n",
"p_safe_24_hours = p_safe_one_hour ** 24\n",
"\n",
"# Probability of being overwhelmed AT LEAST ONCE in 24 hours\n",
"p_overwhelmed_24_hours = 1 - p_safe_24_hours\n",
"\n",
"print(f\"Probability of being overwhelmed at least once in 24 hours: {p_overwhelmed_24_hours:.4f}\")\n",
"print(f\"That's about {p_overwhelmed_24_hours*100:.2f}%\")"
]
},
{
Expand Down Expand Up @@ -155,12 +268,38 @@
"What is the probability that the next customer will arrive within the next 5 minutes?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exponential distribution"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of next customer arriving within 5 minutes: 0.3935\n",
"That's about 39.35%\n"
]
}
],
"source": [
"from scipy.stats import expon\n",
"# Parameters\n",
"mean_arrival = 10 # average time between arrivals (in minutes)\n",
"\n",
"# P(next customer arrives within 5 minutes)\n",
"probability = expon.cdf(5, scale=mean_arrival)\n",
"\n",
"print(f\"Probability of next customer arriving within 5 minutes: {probability:.4f}\")\n",
"print(f\"That's about {probability*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +312,25 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of an employee taking a break: 0.2231\n",
"That's about 22.31%\n"
]
}
],
"source": [
"# P(no customer for 15 minutes) = P(next arrival takes MORE than 15 minutes)\n",
"probability_break = expon.sf(15, scale=mean_arrival)\n",
"\n",
"print(f\"Probability of an employee taking a break: {probability_break:.4f}\")\n",
"print(f\"That's about {probability_break*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
Expand All @@ -194,13 +348,39 @@
"- If we randomly select a bird, what is the probability that its weight is between 140 and 160 grams?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Normal distribution"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 11,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of weight between 140 and 160 grams: 0.6827\n",
"That's about 68.27%\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import norm\n",
"\n",
"# Parameters\n",
"mu = 150 # average weight\n",
"sigma = 10 # standard deviation\n",
"\n",
"# P(140 <= weight <= 160)\n",
"probability = norm.cdf(160, mu, sigma) - norm.cdf(140, mu, sigma)\n",
"\n",
"print(f\"Probability of weight between 140 and 160 grams: {probability:.4f}\")\n",
"print(f\"That's about {probability*100:.2f}%\")"
]
},
{
Expand All @@ -219,11 +399,28 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 12,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Probability of failing within 30 hours: 0.4512\n",
"That's about 45.12%\n"
]
}
],
"source": [
"#code here"
"\n",
"# Parameters\n",
"mean_lifetime = 50 # average lifetime in hours\n",
"\n",
"# P(fails within 30 hours) = P(lifetime <= 30)\n",
"probability = expon.cdf(30, scale=mean_lifetime)\n",
"\n",
"print(f\"Probability of failing within 30 hours: {probability:.4f}\")\n",
"print(f\"That's about {probability*100:.2f}%\")"
]
}
],
Expand All @@ -243,7 +440,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.14.2"
}
},
"nbformat": 4,
Expand Down