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.

Experiment 1:

E1: Toss a true coin three times and observe the sequence of heads and tails.
Total sample space {2}^{3} = 8

Continue reading “Probability | Lecture 1 | Fundamental of Statistic”


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

Continue reading “Introduction to Probability Theory”

How many regions do N lines divide a plane?


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


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.
Continue reading “The Josephus Problem”

The Tower of Hanoi Solution


The Tower of Hanoi problem is a puzzle which can be solved by mathematically and can be implemented in programming code as well. The tower is also called Tower of Brahma or Lucas’ Tower. In this, game there are three pegs and one one of them hold n disks. n disks are ordered from higher radius to lower radius from the bottom to top.
Continue reading “The Tower of Hanoi Solution”