Monte - Carlo Simulation

In this blog, I am going to use simulation for solving famous probability question. We are going to use python’s random number generator to solve the question.

Its a two step process

• Generate the sample
• Count the relevent samples

The Famous Monte-Hall Problem

One hundred people line up to board an airplane. Each has a boarding pass withassigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats at random otherwise. What is the probability that the last person to board gets to sit in his assigned seat?

The expected distance between two points randomly sampled inside a unit square

Estimate the value of pi, euler’s number (e)

Three points are chosen on the unit circle. What is the probability that the origin lies inside the triangle determined by the three points?

What is the probability that a random chord length is greater than radius?

N letters are randomly put into envelops, On an average how many letters are put into its own envelop?

If a stick is broken at random points, what is the expected length of smaller one, ratio of bigger/smaller?