2. Math & Statistics - Probability

Question 1

What is sample space?

Answer 1

The elementary outcomes, which together comprise the sample space, constitute the ultimate breakdown of the potential results of an experiment. For instance, in rolling a die, the elementary outcomes are the points 1, 2, 3, 4, 5, and 6, which together constitute the sample space.

Question 2

How to denote the sample space?

Answer 2

The sample space by S
The elementary outcomes by e1, e2, e3, …
Events by A, B, and so on

Question 3

What does probability study?

Answer 3

Randomness

Question 4

What is probability?

Answer 4

Probability is the proportion of a certain occurrence in a long run (only in large number of occurrences).

Question 5

What is the proportion of occurrence?

Answer 5

1 / sample space

Question 6

What is the probability of both events to happen?

Answer 6

P(A and B) = P(A) * P(B)

Question 7

What is the probability of event A or B to happen?

Answer 7

P(A or B) = P(A) + P(B) - P(A and B)

Question 8

What is P(A subscript C)

Answer 8

P(A subscript C) = 1 - P(A)

Question 9

What kind of letters does events use?

Answer 9

Notation of probability events usually alphabets letters from the begging of alphabet

Question 10

Qual a formula de intersecção de probabilidade?

Answer 10

P(A intersecção B) = P(A) * P(B)

Question 11

O que é a probabilidade de um evento condicional?

Answer 11

É a probabilidade de um evento acontecer, dado a ocorrência de outro evento.

Question 12

Como representar evento condicional?

Answer 12

P(A | B)

If we want to express the probability of one event happening given another one has already happened, we use the “|” symbol to mean “given.”

Question 13

Como calcular eventos condicionais?

Answer 13

P (A | B) = P(A or B) / P(B)

Question 14

Qual método pode ser utilizado para visualizar eventos de probabilidade independentes?

Answer 14

Venn Diagram

Question 15

Qual técnica pode ser utilizada para visualizar eventos de probabilidade condicionais?

Answer 15

Árvore de probabilidade

Question 16

What is the key to creating a good sample?

Answer 16

Choose one that is as close a match to your population as possible.

If your sample is representative, this means it has similar characteristics to the population. And this, in turn, means that you can use your sample to predict what characteristics the population will have.

Question 17

Quando usar a probabilidade convencional?

Answer 17

Quando estivermos lidando com variáveis discretas e eventos independentes.

Question 18

Quando usar a probabilidade Bayesiana?

Answer 18

Quando estivermos lidando com eventos dependentes.

Question 19

Quando usar a probabilidade baseada na “Central Theorem Limit”

Answer 19

Quando estivermos lidando com variáveis quantitativas contínuas.

Question 20

Quais as condições de um evento probabilístico?

Answer 20

1. Mutuamente exclusivo
2. Independente
3. Condicional

Question 21

O que é um Evento Independente?

Answer 21

each event is not affected by other events

Question 22

O que é um Evento Dependente ou Condicional?

Answer 22

an event is affected by other events

Question 23

O que é um Evento Mutuamente Excludente?

Answer 23

events can’t happen at the same time

Question 24

Qual é outra forma de escrever P(A união B)

Answer 24

P(A or B)

Question 25

Qual é outra forma de escrever P(A intersecção B)

Answer 25

P(A and B)

Question 26

Qual a probabilidade de P(A or B) quando A e B são eventos “Mutually Exclusive”?

Answer 26

P(A or B) = P(A) + P(B)

Question 27

Qual a probabilidade de P(A or B) quando A e B não são eventos “Mutually Exclusive”?

Answer 27

P(A or B) = P(A) + P(B) - P(A and B)

Question 28

Qual a probabilidade de eventos compostos independentes?

Answer 28

A probabilidade de dois ou mais eventos independentes é o produtos dos eventos.

P(A) * P(B)