1.1 Probability Distributions We had introduced the concepts of a probability function and random variables in our last editorial. Probability distributions describe what we think the probability of each outcome is, which is sometimes more interesting to know than simply which single outcome is most likely. They come in many shapes, but in only one size:… Continue reading
Category: Pre-College Mathematics
Week -14 | Probability Theory – 2
1.1 Baye’s Theorem For mutually exclusive and exhaustive events , for and an event E, we have the following formula for the probability of given that event E has happened: This is what is known as Baye’s Theorem or the theorem of inverse Probability. Ex -1 A bag A contains 2 white balls and 3… Continue reading
Week -14 | Probability Theory – 1
1.1 An Introduction to Probability In basic mathematical terminology, probability of an event is described as the ratio of the favourable chances of that event to take place, and the total number of chances. This ratio, is a number between 0 and 1. In ideal cases, a probability of an event being 1 will refer… Continue reading
Week -13 | Combinatorics – 10
This is an optional module for those appearing only for the Engineering exams. Practice Problems Q-1) Find the number of 2 digit positive integers that are divisible by both of their digits. Q-2) How many ways are there to arrange the numbers 1,2,3…,64 on a 8×8 chessboard such that the numbers in each row and… Continue reading
Week -13 | Combinatorics – 9
In this module, we’d discuss a couple of counting strategies that maybe useful while solving problems related to the Olympiads. We’d illustrate these strategies with the help of examples. Ex-1) Let be integers greater than 1. Consider to be a set with elements, and let be subsets of . Assume that for any 2 elements , there… Continue reading