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
Tag: CMI
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
Week – 12 | Combinatorics – 7
This is an optional module for students preparing for the engineering entrance exams. Q-1) Among 6 persons in a room, there are either 3 who know each other or 3 who are complete strangers Solution : Let us consider a hexagon with each person denoting a specific vertex of the hexagon. We join 2 vertices… Continue reading
Week -12 | Combinatorics – 5
1.1 Principle of Inclusion and Exclusion This very important principle is a generalization of the Sum Rule to sets which need not be disjoint. Let’s say that we have 2 sets & . We look at the cardinality of the union of these 2 sets (We assume that students going through this module are familiar with… Continue reading