Probability Discrete Math

{1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd?

{1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd?

Matias Aguirre
2022-07-16
Answered

Probability Discrete Math

{1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd?

{1,2,3,4,5,6,7,8,9} What is the probability that the sum of any of these three numbers is odd?

You can still ask an expert for help

asked 2021-08-15

How many elements are in the set
{ 0, { { 0 } }?

asked 2021-08-02

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:$\cap \cup$

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:

asked 2020-11-09

Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.

asked 2021-08-18

Discrete Mathematics Basics

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where$(a,b)\in R$ if and only if

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

asked 2022-06-14

matrix representation of relations over $A=\{1,2,3,\dots ,1000\}$

I have an exercise in discrete math about matrix representation of relations that I want to be sure I have solved properly:

How many non-zero entries does the matrix representing the following relations on $A=\{1,2,3,\dots ,1000\}$ consisting of the first 1000 positive integers have if R is:

a) $R=\{(a,b)\mid a+b=1000\}$

b) $R=\{(a,b)\mid a+b\le 1001\}$

c) $R=\{(a,b)\mid a\ne 0\}$

In the c case, one million since every entry will be 1.

In the a case, every entry, from the first one to the 999-th one, excluding the 1000th row, will have one non-zero entry, so 999

In the b case the whole first row satisfies the condition, the whole second row satisfies the condition and in the third row everything but the entry (3,999) satisfies the condition. In the fourth, everything but (4,999) and (4,998) satisfies the condition.

So we will have $1000+1000+999+998+\mathrm{997...}+1$ non-zero entries in the matrix representing the relation. $999+998+\mathrm{997...}+1=99(100)/2$

So we have $499500+2000=501500$ non zero-entries.

Is this the right way to solve the exercise?

I have an exercise in discrete math about matrix representation of relations that I want to be sure I have solved properly:

How many non-zero entries does the matrix representing the following relations on $A=\{1,2,3,\dots ,1000\}$ consisting of the first 1000 positive integers have if R is:

a) $R=\{(a,b)\mid a+b=1000\}$

b) $R=\{(a,b)\mid a+b\le 1001\}$

c) $R=\{(a,b)\mid a\ne 0\}$

In the c case, one million since every entry will be 1.

In the a case, every entry, from the first one to the 999-th one, excluding the 1000th row, will have one non-zero entry, so 999

In the b case the whole first row satisfies the condition, the whole second row satisfies the condition and in the third row everything but the entry (3,999) satisfies the condition. In the fourth, everything but (4,999) and (4,998) satisfies the condition.

So we will have $1000+1000+999+998+\mathrm{997...}+1$ non-zero entries in the matrix representing the relation. $999+998+\mathrm{997...}+1=99(100)/2$

So we have $499500+2000=501500$ non zero-entries.

Is this the right way to solve the exercise?

asked 2022-05-27

Slope if true or false and also provide a verson.

Every union of disconnected subset of a metric space is disconnected.

Every union of disconnected subset of a metric space is disconnected.

asked 2021-08-17

Discrete math

Given$U=\{1,2,3,4,5,6,7,8,9,10\},{S}_{1}=\{1,3,5,7,9\},{S}_{2}=\{1,2,4,6,8,10\}$ . What is the $S}_{1}\cap {S}_{2$ in bit strings?

Select one :

1) 00

2) 01

3) 0000000000

4) 0000000001

5) 1000000000

Given

Select one :

1) 00

2) 01

3) 0000000000

4) 0000000001

5) 1000000000