L1 - Probability Flashcards Preview

18ECA005 - Data Analysis II > L1 - Probability > Flashcards

Flashcards in L1 - Probability Deck (13)
Loading flashcards...
1

How is Outcome defined?

- he basic result of a chance situation. All the possible
outcomes = sample space.

Ex: the numbers 1 to 6 when throwing a die

2

When are Outcomes Mutually Exclusive?

- They cannot happen at the same
time, at each trial
= Ex: I cannot get a 3 and a 4 in one throw of a die.
- Therefore P(A∩B) = 0

- Since outcomes are mutually exclusive and they exhaust all possible
- “results” their probabilities sum to 1, or 100%

Ex: 100% probability to get either head or tail

3

How is an Experiment defined?

a generic activity (flipping a coin or throwing a die)

4

How is a Trial defined?

a single performance of the experiment.

5

How is an Event defined?

An event is a collection of outcomes.
Ex: in the experiment of throwing a die define the event “even
number” (either 2, or 4 or 6). The probability of an event is the sum of the probabilities of its outcome

6

How are Complementary Events defined?

- Complementary events: mutually exclusive events that are also the
exact negation of one another: A and B are complementary if B is “nonA”. Ex: employed and unemployed. -Complementary events must cover the whole sample space, so P(A)+P(B)=1.
- As Complementary events are mutually exclusive events that are also one
the opposite of the other: P(A) = 1-P(B) and vice versa

This is not true for all
mutually exclusive events:

Ex: 3 categories of age: < 30 , 30-40, and > 40. Each pair is mutually exclusive but not complementary ( not being < 30 does not necessarily mean that you are > 40)

7

What is Priori Probability?

- the outcomes are equally likely e.g. probability of getting a heads or tails
- this also works if each of the different things have an equal chance of being picked or have equal outcome even though they have different 'weights' e.g. winning lottery tickets still have the same outcome of being picked so are priori probability

- P(event) = (number of outcome occurring in the event)/( total number of outcomes)

8

What is Experimental Probability?

- Also know as Empirical Probability
- Outcomes are not equally likely and/or lack knowledge to make a judgement
- We make experiments using samples and make inference
- As the number of trials increases the
estimated probability will get very close to the “true” probability

9

What is Intuitive Probability?

- Also know as Subjective Probability
-This is the “educated guess” made with no theoretical grounds nor specific
data.

Ex: when we decide whether it is going to rain or not. We do use our
general experience but have no way of formalising it, and the judgement is
subjective.

10

What is the "AND" operator?

- A compound event is the combination of two or more events to create more elaborate one
- Intersection of events --> The events must happen at the same time Symbolically ∩
- The probability of an AND event is called a joint probability

11

What is the "OR" operator?

- Union of events --> If we define two events A and B
their union is a third larger one that comprises them both. This means that
either A happens, or B happens or both. Symbolically ∪

12

What is the Additional Rule?

- Sometimes you can easily sum the probabilities of the outcomes
comprised in the event

- the addition rule is as follows:
- P(A∪B) = P(A)+P(B) - P(A∩B)
- P(A∩B) = P(A)+P(B) - P(A∪B)
This is always true, regardless of whether events are dependent or
independent

13

What is the Multiplication Rule?

- if events are independent, i.e. the probability of
one does not affect that of the other, then the probability of joint events
can be calculated as:

P(A∩B) = P(A)*P(B)

If events are dependent this has to be modified slightly