LM 02

Question 1

Definition of the probability of equally likely outcomes

Answer 1

Assume that there are N outcomes, all of which are equally likely to occur, then, the probability of each outcome is 1/N, and the probability of an event containing exactly n outcomes is n/N. We write this as P(A)

Question 2

How do probabilities sum?

Answer 2

I’ll probabilities must come to one or 100%

Question 3

Probability definition

Answer 3

The probability of an outcome is the proportion of times the outcome would occur if we observe the random process an infinite number of times

Question 4

Three steps to find the probability

Answer 4

1) define an event
2) find out the outcomes in the event
3) sum up their probabilities

Question 5

Mutually exclusive or disjoint

Answer 5

Two events are considered mutually exclusive or disjoint if they have no outcomes in common

Question 6

Another way of writting P(A or B)

Answer 6

P(A u B)

Question 7

Another way of writing P(A and B)

Answer 7

P (A n B)

Question 8

Addition rule ( An and B are disjoint events)

Answer 8

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

Question 9

General addition rule ( A and B are disjoint or not)

Answer 9

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

Question 10

Outcome

Answer 10

Random result from experiment

Question 11

Event

Answer 11

Set of outcomes, has probability assigned to it

Question 12

Sample space

Answer 12

All possible outcomes

Question 13

Complement

Answer 13

Probability that the event does not occur

Question 14

Complement rule

Answer 14

The compliment of A, denoted by A^c, is an event that contains all outcomes in the sample space that are not in A.
P(A^c) = 1-P(A)

Question 15

Conditional Probability

Answer 15

Conditional upon the fact that we know event be, what is the probability of event a. This is noted as P(A|B).
P(A|B) = P(A n B)/P(B)
Or
P(A|B) = P(A n B)/ (P(A n B)+P(A^c n B))

Question 16

Multiplication Rule

Answer 16

P(A n B) = P(A) P(B|A) = P(B)P(A|B)

Question 17

Bayes Therem

Answer 17

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

Question 18

Multiplication Rule (independent events)

Answer 18

P(A n B) = P(A) P(B)

Question 19

Independent Events

Answer 19

If learning that one of event occurred tells us nothing about whether the other event occurred. To check independence you solve to see if P(A n B) = P(A) P(B). If true A and B are independent and P(A|B) = A and P(B|A) = B

Question 20

Tree diagrams

Answer 20

A tool to organize outcomes and probabilities.