Tutorial on finding the probability of an event. In what follows, S is the sample space of the experiment in question and E is the event of interest. Free Mathematics Tutorials. Probability Questions with Solutions Tutorial on finding the probability of an event. Questions and their Solutions Question 1 A die is rolled, find the probability that an even number is obtained. Solution Let us first write the sample space S of the experiment.

More Info. Top Menu. Follow Us. All rights reserved. Privacy Policy. Note: Each coin has two possible outcomes H heads and T Tails. Solution The sample space S is given by. Question 4 Two dice are rolled, find the probability that the sum is a equal to 1 b equal to 4 c less than 13 Solution a The sample space S of two dice is shown below.

**[Discrete Mathematics] Nonhomogeneous Recurrence Relations**

Solution Let H be the head and T be the tail of the coin. Find the probability of getting the 3 of diamond. Solution The sample space S of the experiment in question 6 is shwon below Let E be the event "getting the 3 of diamond". Find the probability of getting a queen. Solution The sample space S of the experiment in question 7 is shwon above see question 6 Let E be the event "getting a Queen". If a marble is drawn from the jar at random, what is the probability that this marble is white?

Solution We first construct a table of frequencies that gives the marbles color distributions as follows color frequency red.In an undirected graph, the numbers of odd degree vertices a re even. As left hand side of equation 1 is even and the first expression on the RHS of 1 is even, we have the 2nd expression on the RHS must be even.

Since each deg vj is odd, the number of terms contained in i. If the simple graph G has 4 vertices and 5edges, then how many edges does Gc have? How many edges are there in a graph with ten vertices each of degree six.

There are 30 edges. MA Notes Discrete Mathematics. What are the eight great ideas in computer architecture? What are the five classic components of a computer? What is the function of data […]. Electronic Circuits 1 Important questions EC pdf free download. Define noise Noise is an unwanted electrical signal which gets added tom a transmitted signal when it is travelling towards the receiver […]. What are the various types of memory in embedded systems? Your email address will not be published.

Leave this field empty. Related Articles. Important question. Posted on December 19, December 19, Author Mr. Posted on April 28, April 28, Author Mr. Posted on May 7, May 7, Author Mr. Leave a Reply Cancel reply Your email address will not be published.If you are an expert in problem solving and reasoning techniques, then you can make a career in discrete mathematics. The modern world of computer science is mainly built around discrete mathematics. As a user of discrete mathematicsyou can study topics such as integers, graphs and statements which involve a lot of logic.

Wisdomjobs helps you to find job opportunities where you can get a chance to work on computer languages, cryptography and software development which all require the knowledge of discrete mathematics.

We also help you to get an idea about the necessary qualifications and skills required to become a specialized user. Further our team of experts have made a list of discrete mathematics job interview questions and answers to help you to crack the job interview easily and climb up in your career. Question 1.

What Is Discrete Mathematics? Answer : Discrete Mathematics is a branch of mathematics involving discrete elements that uses algebra and arithmetic. It is increasingly being applied in the practical fields of mathematics and computer science. It is a very good tool for improving reasoning and problem-solving capabilities. Question 2.

It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers.

### MA6566 Discrete Mathematics previous year question papers

For example, a function in continuous mathematics can be plotted in a smooth curve without breaks. For example, if we have a finite set of objects, the function can be defined as a list of ordered pairs having these objects, and can be presented as a complete list of those pairs. Question 3. Answer : A set is an unordered collection of different elements.

A set can be written explicitly by listing its elements using set bracket. If the order of the elements is changed or any element of a set is repeated, it does not make any changes in the set.

Question 4. Roster or Tabular Form: The set is represented by listing all the elements comprising it. The elements are enclosed within braces and separated by commas.

Set Builder Notation: The set is defined by specifying a property that elements of the set have in common. Question 5.Antisymmetric Bisymmetric Anti reflexive.

The number of regions corresponds to the cyclomatic complexity. Share to:. A graph G is called a What is the probability of choosing correctly an unknown integer between 0 and 9 with 3 chances? In an undirected graph the number of nodes with odd degree must be. A graph is a collection of. Vertices and edges. An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are.

How many relations are there on a set with n elements that are symmetric and a set with n elements that are reflexive and symmetric?

The number of colours required to properly colour the vertices of every planer graph is. In how many ways can a president and vice president be chosen from a set of 30 candidates? Consider an undirected random graph of eight vertices. What is the expected number of unordered cycles of length three?

A minimal spanning tree of a graph G is. All of above. The number of leaf nodes in a complete binary tree of depth d is. A partial ordered relation is transitive, reflexive and. In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities?

A graph with n vertices will definitely have a parallel edge or self loop if the total number of edges are. A vertex of a graph is called even or odd depending upon. Total number of edges in a graph is even or odd. Total number of vertices in a graph is even or odd. Its degree is even or odd. In any undirected graph the sum of degrees of all the nodes. Are twice the number of edges. A graph with one vertex and no edges is.

Length of the walk of a graph is. The number of edges in walk W.The set of positive integers excluding zero with addition operation is a semigroup. A monoid is a semigroup with an identity element. An identity element is also called a unit element. The set of positive integers excluding zero with multiplication operation is a monoid.

Here identity element is 1. A group is a monoid with an inverse element. So, a group holds four properties simultaneously - i Closure, ii Associative, iii Identity element, iv Inverse element. The order of a group G is the number of elements in G and the order of an element in a group is the least positive integer n such that an is the identity element of that group G. As all the matrices are non-singular they all have inverse elements which are also nonsingular matrices.

Hence, inverse property also holds. So, a group holds five properties simultaneously - i Closure, ii Associative, iii Identity element, iv Inverse element, v Commutative. The set of positive integers including zero with addition operation is an abelian group. Here, identity element is 1. A cyclic group is a group that can be generated by a single element. Every element of a cyclic group is a power of some specific element which is called a generator.

Hence, it is a cyclic group. The rational numbers under addition is not cyclic but is abelian. A subgroup of a cyclic group is cyclic and a abelian subgroup is also abelian. A partially ordered set consists of a set with a binary relation which is reflexive, antisymmetric and transitive. The Hasse diagram of a poset is the directed graph whose vertices are the element of that poset and the arcs covers the pairs x, y in the poset.

A Linearly ordered set or Total ordered set is a partial order set in which every pair of element is comparable. Trichotomy law defines this total ordered set. Hence, it is not a total ordered set.

## EECS 203: Discrete Mathematics

A lattice L becomes a complemented lattice if it is a bounded lattice and if every element in the lattice has a complement. If a lattice satisfies the following two distribute properties, it is called a distributive lattice. Discrete Mathematics - Group Theory Advertisements.

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### MA8351 DM 2marks 16marks, Discrete Mathematics Question Bank, DM Short Answers

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Answer - Click Here: C. In how many ways can a hungry student choose 3 toppings for his prize from a list of 10 delicious possibilities? In any, undirected graph the sum of degrees of all the nodes A. Must be even B. Are twice the number of edges C. Must be odd D. Need not be even. The walk of a graph length is: A. The number of vertices in walk W B. Total number of vertices in a graph C.

Total number of edges in a graph D. The number of edges in walk W. Definition of a plane graph is: A. A graph, drawn in a plane in such a way that any pair of edges meet only at their end vertices B.

A graph, drawn in a plane in such a way that if the vertex set of the graph can be partitioned into two non — empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y C. A simple graph which is Isomorphic to Hamiltonian graph D. A continuous non-intersecting curve in the plane whose origin and terminus coincide : A. Jordan B. Planer C.

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