# Probability | Lecture 1 | Fundamental of Statistic

Experiment: Experiment is a process of observation. Here, we will use E to denote it.

Sample Space: The set of all possible outcome of the experiment. We will use S to denote it.

# Introduction to Probability Theory

### Sample Space and Events

The set of all possible outcome of an experiment while the precise outcome is unknown is called Sample Space and it is often denoted by S.

For a single coin: Sample Space, $S = \lbrace H, T \rbrace$
For two coins, Sample Space, $S = \lbrace (H, H),(H,T),(T,H),(T,T) \rbrace$
For a rolling dice, Sample Space, $S = \lbrace 1,2,3,4,5,6 \rbrace$

# Prove that, there are infinite number of prime numbers.

Proof: Let’s assume there are finite number of prime numbers. Then let the greatest prime number is N.

# How many regions do N lines divide a plane?

### Explanations:

N straight lines are drawn on a plane paper. Each line intersects with rest all lines. That means N‘th line intersects N-1lines. You can assume infinite number of lines can be drawn on that paper. You have to find total regions after N lines are drawn. An image is given below to understand the problem clearly.
Continue reading “How many regions do N lines divide a plane?”

# The Josephus Problem

### Introduction

The Josephus Problem is a count-out game which is regarded as a theoretical problem in Computer Science or Mathematics. In this game, n people stand in a circle s is the starting number of people. s is holding a sword where skills s+k-1‘th people from his position and gives his sword to s+k‘th people. Thus s+k becomes new s. Going in the same direction this procedure is repeated until one person is left. Remaining one person is marked as a winner.