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58 changes: 27 additions & 31 deletions README.md
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@@ -1,54 +1,50 @@
![logo_ironhack_blue 7](https://user-images.githubusercontent.com/23629340/40541063-a07a0a8a-601a-11e8-91b5-2f13e4e6b441.png)

# Lab | Introduction to Probability
# Laboratorio | Introducción a la Probabilidad

<details>
<summary>
<h2>Learning Goals</h2>
</summary>
<summary>
<h2>Objetivos de Aprendizaje</h2>
</summary>

This exercise allows you to practice and apply the concepts and techniques taught in class.
Este ejercicio te permite practicar y aplicar los conceptos y técnicas enseñados en clase.

Upon completion of this exercise, you will be able to:

- Identify different probabilities distributions.
- Calculate pmf/cdf for given problems.

<br>
<hr>
Al completar este ejercicio, podrás:

</details>

<details>
<summary>
<h2>Prerequisites</h2>
</summary>
Before this starting this lab, you should have learnt about:

- Basic Probabilities concepts.
- Understand difference between distributions and where/how to apply them in a business context.
- Identificar diferentes distribuciones de probabilidad.
- Calcular pmf/cdf para problemas dados.

<br>
<hr>
<br>
<hr>

</details>

## Introduction
<details>
<summary>
<h2>Requisitos Previos</h2>
</summary>
Antes de comenzar este laboratorio, deberías haber aprendido sobre:

In this exercise, you will have the opportunity to dive into one of the fundamental of probability.
- Conceptos básicos de probabilidad.
- Entender la diferencia entre distribuciones y dónde/cómo aplicarlas en un contexto empresarial.

<br>
<hr>

**Happy coding!** :heart:
</details>

## Introducción

En este ejercicio, tendrás la oportunidad de profundizar en uno de los fundamentos de la probabilidad.

<br>

## Getting Started
**¡Feliz programación!** :heart:

Complete the challenges in the notebook. Follow the instructions and add your code and explanations as necessary.
## Comenzando

Completa los desafíos en el cuaderno. Sigue las instrucciones y agrega tu código y explicaciones según sea necesario.

## Submission
## Entrega

- Submit your solutions in the Student Portal.
- Envía tus soluciones en el Portal del Estudiante.
186 changes: 161 additions & 25 deletions lab-intro-probability.ipynb
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Expand Up @@ -38,11 +38,39 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"(np.float64(0.884477246621543), np.float64(88.4477246621543))"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"from scipy.stats import binom\n",
"\n",
"n = 460 # tickets vendidos\n",
"p = 0.03 # prob. de no presentarse\n",
"\n",
"# P(X >= 10) donde X ~ Bin(n, p)\n",
"prob_seats_for_all = binom.sf(9, n, p) # sf(9) = P(X > 9) = P(X >= 10)\n",
"\n",
"prob_seats_for_all, prob_seats_for_all*100\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"✅ Si venden 460 tickets, hay ~88.45% de chances de que al menos 10 no se presenten, y entonces entran todos en los 450 asientos.\n",
"\n",
"✅ El riesgo de overbooking real sería el complemento: 1 − 0.8844772466 = 0.1155227534 → 11.55%."
]
},
{
Expand Down Expand Up @@ -72,11 +100,24 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 2,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"(0.48999999999999994, 48.99999999999999)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"p = 0.3\n",
"prob_at_least_3_attempts = (1 - p)**2\n",
"prob_at_least_3_attempts, prob_at_least_3_attempts*100\n"
]
},
{
Expand Down Expand Up @@ -107,11 +148,29 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 3,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"(np.float64(0.012898220840392027), np.float64(1.2898220840392027))"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"from scipy.stats import poisson\n",
"\n",
"lam = 500\n",
"\n",
"# P(X > 550) = sf(550)\n",
"p_overwhelmed_1h = poisson.sf(550, lam)\n",
"\n",
"p_overwhelmed_1h, p_overwhelmed_1h*100\n"
]
},
{
Expand All @@ -123,11 +182,24 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 4,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"(np.float64(0.2677043869515715), np.float64(26.77043869515715))"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"p_overwhelmed_day = 1 - (1 - p_overwhelmed_1h)**24\n",
"\n",
"p_overwhelmed_day, p_overwhelmed_day*100\n"
]
},
{
Expand Down Expand Up @@ -157,10 +229,30 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"data": {
"text/plain": [
"(0.3934693402873666, 39.346934028736655)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import math\n",
"\n",
"lam = 1/10 # tasa por minuto\n",
"t = 5\n",
"\n",
"p_within_5 = 1 - math.exp(-lam*t)\n",
"\n",
"p_within_5, p_within_5*100\n"
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +265,27 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"data": {
"text/plain": [
"(0.22313016014842982, 22.313016014842983)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = 15\n",
"\n",
"p_break = math.exp(-lam*t)\n",
"\n",
"p_break, p_break*100\n"
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +305,26 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 8,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"292201338"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"import math\n",
"\n",
"total_combinations = math.comb(69, 5) * math.comb(26, 1)\n",
"\n",
"total_combinations\n"
]
},
{
Expand All @@ -219,11 +343,23 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 9,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"(3.4222978130237033e-09, 3.4222978130237034e-07)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#code here"
"prob_win = 1 / total_combinations\n",
"prob_win, prob_win*100\n"
]
}
],
Expand All @@ -243,7 +379,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.14.0"
}
},
"nbformat": 4,
Expand Down