supix · June 19, 2018 07:11 · Jun 19, 2018 · Jun 19, 2018 · Jun 19, 2018 · Jun 19, 2018
diff --git a/Bayes.md b/Bayes.md
@@ -107,4 +107,4 @@ Running the code we have: 0,35584
 
 # Acknowledgement
 
-Thanks to [Julia](https://www.youtube.com/watch?v=BrK7X_XlGB8) for inspiring me this riddle.
+Thanks to [Julia](https://www.youtube.com/watch?v=BrK7X_XlGB8) for having inspired this riddle.
diff --git a/Bayes.md b/Bayes.md
@@ -44,20 +44,23 @@ namespace Bayes
 {
     internal class Program
     {
+        private const double totalStudents = 1e6;
+        private const double studentsToPick = 1e5;
+
         private static void Main(string[] args)
         {
             var rnd = new Random();
             var people = new List<Student>();
 
-            for (int i = 0; i < 1e7; i++)
+            for (int i = 0; i < totalStudents; i++)
             {
                 people.Add(Student.Create());
             }
 
             int selectedShys = 0;
             int mathStudents = 0;
 
-            for (int i = 0; i < 1e6; i++)
+            for (int i = 0; i < studentsToPick; i++)
             {
                 var s = people[rnd.Next(people.Count)];
                 if (s.Shy)

diff --git a/Bayes.md b/Bayes.md
@@ -75,11 +75,14 @@ namespace Bayes
 
     public class Student
     {
+        private const double probToBeMathStudent = .1d;
+        private const double probToBeShyGivenMath = .75d;
+        private const double probToBeShyGivenBA = .15d;
+        private static Random rnd = new Random();
+
         public bool Math { get; }
         public bool Shy { get; }
 
-        private static Random rnd = new Random();
-
         public Student(bool math, bool shy)
         {
             this.Math = math;
@@ -88,8 +91,8 @@ namespace Bayes
 
         public static Student Create()
         {
-            var math = rnd.NextDouble() < .1d;
-            var shy = math ? rnd.NextDouble() < .75d : rnd.NextDouble() < .15d;
+            var math = rnd.NextDouble() < probToBeMathStudent;
+            var shy = math ? rnd.NextDouble() < probToBeShyGivenMath : rnd.NextDouble() < probToBeShyGivenBA;
 
             return new Student(math, shy);
         }

diff --git a/Bayes.md b/Bayes.md
@@ -31,7 +31,7 @@ Doing the math we have an overall probability of 0.3571428.
 
 # Solution through the [Frequentist Probability](https://en.wikipedia.org/wiki/Frequentist_probability)
 
-This piece of code, written in C#, prints the probability of picking a shy student he happens to be a math student.
+This piece of code, written in C#, prints the probability that picking a shy student he happens to be a math student.
 
 ```csharp
 using System;

diff --git a/Bayes.md b/Bayes.md
@@ -5,7 +5,7 @@ Within math faculty, 75% students are shy. Within business administration, 15% s
 
 # Problem
 
-I see a student, and he is clearly shy. What's the probability that he is enrolled in math faculty.
+I see a student, and he is clearly shy. What's the probability that he is enrolled in math faculty?
 
 # Theoretical solution through Bayes Theorem
 

diff --git a/Bayes.md b/Bayes.md
@@ -31,7 +31,7 @@ Doing the math we have an overall probability of 0.3571428.
 
 # Solution through the [Frequentist Probability](https://en.wikipedia.org/wiki/Frequentist_probability)
 
-This piece of code, written in C#, prints the probability of picking a math student given that he is shy.
+This piece of code, written in C#, prints the probability of picking a shy student he happens to be a math student.
 
 ```csharp
 using System;

diff --git a/Bayes.md b/Bayes.md
@@ -19,7 +19,7 @@ P(Math|Shy) = -----------------------
                      P(Shy)
 ```
 
-From data stem that:
+From data it stems that:
 
 ```
 P(Shy|Math) = 0.75

diff --git a/Bayes.md b/Bayes.md
@@ -97,4 +97,8 @@ namespace Bayes
 }
 ```
 
-Running the code we have: 0,35584
+Running the code we have: 0,35584
+
+# Acknowledgement
+
+Thanks to [Julia](https://www.youtube.com/watch?v=BrK7X_XlGB8) for inspiring me this riddle.
diff --git a/Bayes.md b/Bayes.md
@@ -5,7 +5,7 @@ Within math faculty, 75% students are shy. Within business administration, 15% s
 
 # Problem
 
-I see a student, and he is clearly shy. What's the probability that he applies to math faculty.
+I see a student, and he is clearly shy. What's the probability that he is enrolled in math faculty.
 
 # Theoretical solution through Bayes Theorem
 

diff --git a/Bayes.md b/Bayes.md
@@ -21,13 +21,15 @@ P(Math|Shy) = -----------------------
 
 From data stem that:
 
+```
 P(Shy|Math) = 0.75
 P(Math) = 0.1
 P(Shy) = P(Shy|Math) P(Math) + P(Shy|BA) P(BA) = 0.75 * 0.1 + 0.15 * 0.90
+```
 
 Doing the math we have an overall probability of 0.3571428.
 
-# Solution through the [Frequantist Probability](https://en.wikipedia.org/wiki/Frequentist_probability)
+# Solution through the [Frequentist Probability](https://en.wikipedia.org/wiki/Frequentist_probability)
 
 This piece of code, written in C#, prints the probability of picking a math student given that he is shy.
 

diff --git a/Bayes.md b/Bayes.md
@@ -0,0 +1,98 @@
+# Context
+
+We are in a university campus. There are two faculties: math and business administration. 10% of student are enrolled in math (then, 90% of students are enrolled in business administration).
+Within math faculty, 75% students are shy. Within business administration, 15% students are shy.
+
+# Problem
+
+I see a student, and he is clearly shy. What's the probability that he applies to math faculty.
+
+# Theoretical solution through Bayes Theorem
+
+I have to compute P(Math|Shy).
+
+According to [Bayes theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem), we have:
+
+```
+               P(Shy|Math) P(Math)
+P(Math|Shy) = -----------------------
+                     P(Shy)
+```
+
+From data stem that:
+
+P(Shy|Math) = 0.75
+P(Math) = 0.1
+P(Shy) = P(Shy|Math) P(Math) + P(Shy|BA) P(BA) = 0.75 * 0.1 + 0.15 * 0.90
+
+Doing the math we have an overall probability of 0.3571428.
+
+# Solution through the [Frequantist Probability](https://en.wikipedia.org/wiki/Frequentist_probability)
+
+This piece of code, written in C#, prints the probability of picking a math student given that he is shy.
+
+```csharp
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Bayes
+{
+    internal class Program
+    {
+        private static void Main(string[] args)
+        {
+            var rnd = new Random();
+            var people = new List<Student>();
+
+            for (int i = 0; i < 1e7; i++)
+            {
+                people.Add(Student.Create());
+            }
+
+            int selectedShys = 0;
+            int mathStudents = 0;
+
+            for (int i = 0; i < 1e6; i++)
+            {
+                var s = people[rnd.Next(people.Count)];
+                if (s.Shy)
+                {
+                    selectedShys++;
+                    if (s.Math)
+                        mathStudents++;
+                }
+            }
+
+            Console.WriteLine(mathStudents / (double)selectedShys);
+            Console.ReadLine();
+        }
+    }
+
+    public class Student
+    {
+        public bool Math { get; }
+        public bool Shy { get; }
+
+        private static Random rnd = new Random();
+
+        public Student(bool math, bool shy)
+        {
+            this.Math = math;
+            this.Shy = shy;
+        }
+
+        public static Student Create()
+        {
+            var math = rnd.NextDouble() < .1d;
+            var shy = math ? rnd.NextDouble() < .75d : rnd.NextDouble() < .15d;
+
+            return new Student(math, shy);
+        }
+    }
+}
+```
+
+Running the code we have: 0,35584