Monthly Archives: February 2015

Chess Question on total probability

Posted on February 21, 2015 by Sumant Sumant

You enter a chess tournament where your probability of winning a game is against half of the players (call them type 1), against a quarter of the players (call them type 2) and against the remaining quarter of the players … Continue reading →

Posted in Probability | Leave a comment

Angle bisector theorem proof -2

Posted on February 21, 2015 by Sumant Sumant

Here is another proof of Angle Bisector theorem. This time using only sine rule.There is another proof by extending the bisector.  

Posted in Famous Problem, Geometry, Proof | Leave a comment

What is Independence in Probability, Ranking p,q,r,s

Posted on February 19, 2015 by Sumant Sumant

Intuitively it means that if two event happens successively if the outcome of later event is not affected by the first than the two events are independent. There are advantages to using the second definition Symmetric Suppose we have to … Continue reading →

Posted in Probability | Leave a comment

Disjoint Vs Independence Probability

Posted on February 19, 2015 by Sumant Sumant
Posted in Probability | Leave a comment

Complement of Independent Events are Independent Events

Posted on February 19, 2015 by Sumant Sumant

Suppose that  and  are independent events. Are  and  independent? Given and are independent i.e .

Posted in Probability | Leave a comment

Series Parallel- Reliability Probability

Posted on February 19, 2015 by Sumant Sumant

Suppose that each unit of a system is up with probability  and down with probability . Different units are independent. For each one of the systems shown below, calculate the probability that the whole system is up (that is, that … Continue reading →

Posted in Probability | Leave a comment

Differential Equation Notes

Posted on February 14, 2015 by Sumant Sumant

Why are differential equations important? Differential equations is a beautiful application of the ideas and techniques to our everyday lives. Indeed Calculus was developed so that the fundamental principles that govern many phenomena could be expressed in the language of … Continue reading →

Posted in Differential Equations | Leave a comment

Probability Notes

Posted on February 13, 2015 by Sumant Sumant

What do you understand by the term that sample space should be collectively exhaustive ? The sample space chosen for a probabilistic model must be collectively exhaustive, in the sense no matter what happens in the experiment, we always obtain … Continue reading →

Posted in Probability | Leave a comment

Sum of absolute differences of numbers around a circle

Posted on February 13, 2015 by Sumant Sumant

The first positive integers are spotted around a circle in any order you wish and the positive differences between consecutive pairs are determined. Prove that, no matter how the integers might be jumbled up around the circle, the sum of … Continue reading →

Posted in Inequalities | Tagged , | Leave a comment

10 point inside a circle, British Olympiad, 1983

Posted on February 13, 2015 by Sumant Sumant

If points are chosen in a circle of diameter , prove that the distance between some pair of them is less than

Posted in Geometry, Pegion Hole | Tagged , , | Leave a comment