Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Logics And Argumentation > Probability > Flashcards

Probability Flashcards

1
Q

What is the difference between deductive and inductive logics?

A

In deductive logic the conclusion follows from the premises with certainty i.e. the logic condition is fulfilled and no risk is involved;

In inductive logic the conclusion only follows with some probability, making it a risky inference. The conclusion bears some risk of not following with certainty from valid premises.

Deductive logic is valid only with certainty while inductive is valid if the conclusion is strong.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What does the 3 point triangle mean in logics and mathematics?

A

Therefore

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Which two questions must be answered before an inductive argument can be properly evaluated?

A
  1. How strong in the inference from the premises to the conclusion (what’s is the probability that the conclusion is true, given the premises)?
  2. How high does the probability have do be before it is rational to accept the conclusion
    (What the rational threshold)?
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is the range of a probability function P(A) where P is the probability and A is an event.

A

Between 0 and 1 (0% chance and 100% chance)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Given P(A) and P(B), what does probability theory give us?

A

It gives us the rules for calculating, among others:

P(not-A);

P(A and B);

P(A or B);

P(A given B).

This is probability calculus.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

In the classical interpretation, given a random trial with a set of possible outcomes, what is P(A)?

A

Number of favourable cases (that give A)

Divided by

Total number of equally possible cases.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is the principle of indifference?

A

We should treat a set of outcomes as equally possible if we have no reason to consider one outcome more probable than the other (or others).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

When does the principle of indifference apply?

A

When we have no evidence at all;

When we have symmetrically balanced evidence.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What are the shortcomings of the classical interpretation of probability?

A

Finite number of elementary outcomes;

Equal possibility for each elementary outcome.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Is the classical interpretation of probability good enough as a theory?

A

No, it’s especially good for gambling only.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Define the logical probability interpretation of probability.

A

The degree of logical support that a conclusion has, relative to a set of premises;

i.e.

The degree of confirmation that evidence confers on a hypothesis.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is the frequency theory of probability?

A

E

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is finite relative frequency?

A

When the number of trials is certain and finite. It deals with a finite number of observed trials.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is a limiting relative frequency?

A

When we are asked to consider what the relative frequency would converge to in the long run if we had an infinite number of trials.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What are the shortcomings of frequency interpretation of probability.

A

We cannot know wage will happen in the infinite time frame.

Not suitable for single-case events.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the Bayesian (subjective) theory of probability?

A

A theory that states that probability is subjective to the observer. It tries to assign a number to a persons degree of belief.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is a Dutch book contract?

A

A bet that is a guaranteed loss (sure-loss contract).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the basic rule of Bayesian rationality?

A

No rational person will willingly agreed to a bet that is a sure-loss.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What name is given to set of personal beliefs that is not open to a Dutch book contract?

A

Coherent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What does Bayesian probability used for?
What is the basic Bayes’ rule?
Explain each variable and component of the equation.

A

Normally used to asses the probability of an hypothesis given the evidence - P(H/E).

P(H/E)=(P(H)*P(E/H))/P(E)

H=hypothesis
E=evidence

Where P(H/E) is the posterior probability of H;
P(H) is the prior probability of H;
P(E/H) is the likelihood of the evidence E if H is true;
P(E) is the total probability of E.

21
Q

What is epistemic probability?

Give examples.

A

Is the probability of an event GIVEN certain evidence.

It is based on the evidence available (what we know).

Examples: Logical probability and Bayesian probability interpretations.

22
Q

What is objective (physical) probability?

Give examples.

A

Probability that depends on objective features of nature (the world) that were discovered and not subject to belief disputes.

Examples: classical, frequency-based and propensity interpretations of probability.

23
Q

What is the propensity theory of probability?

A

A theory that proposes that the long-term (limit) value of the probability of an event depends on propensities peculiar to individual events.

24
Q

What are the two languages used to refer to probability?

A

Propositional languages; and

Event language

25
Q

What is proposition language of probability?

Give an example.

A

Used to assess the probability of a proposition, or a claim.

Example: what is the probability that a coin will land heads?

“A coin will land heads” is a proposition

26
Q

What is the event language of probability?

Give an example.

A

Used to assess the probability of an event occurring.

Example: what is the probability of a coming landing heads?

A coin landing heads is not a proposition; it is an event.

27
Q

When are propositional and event languages most appropriate?

A

Propositional language is most appropriate when analysing evidence (philosophers and logicians);

Event language is most appropriate for non-evidence data (statisticians).

28
Q

What is the range of probabilities?

A

Probabilities are real numbers that can take any value between zero and one.

29
Q

What does it mean when the probability of an event is one?

A

It must occur i.e. it is necessarily true.

30
Q

What does it mean when the probability of an event is zero?

A

It cannot occur i.e. it is necessarily false.

31
Q

What does it mean when the probability of an event is between zero and one?

A

It mean it can occur; it is contingently tue or false.

Contingent = possible

32
Q

What are mutually exclusive events (disjoint events)?

A

Events that cannot occur at the same time.

33
Q

What are independent events?

Show with equations.

A

Events whose probabilities are not affected by the occurrence of other events.

P(A given B) = P(A)
P(B given A) = P(B)

If events are dependent than:

P(A given B) not= P(A)

34
Q

What’s the negation rule?

A

P(not-A) = 1 - P(A)

35
Q

What is P(A or B); or what is the (restricted) disjunction rule?

A

P(A) + P(B); or the sum of the probabilities of the disjuncts.
The (restricted) disjunction rule above only works if it is a exclusive disjunction.

36
Q

What is P(A or B) when the disjunction is general (the events are not mutually exclusive?

A

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

37
Q

What does “restricted” mean when talking about probability rules?

A

It means that the possible outcomes are mutually exclusive.

38
Q

What is the (restricted) conjunction rule for independent events?

A

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

When A and B are independent events.

39
Q

What is the (general) conjunction rule for not-independent events?

A

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

Where A and B are dependent events.

P(B/A) : probability of B given A

40
Q

What is a categorical probability?

A

Probability that is not conditional on other events P(A).

41
Q

What is conditional probability?

A

A probability that is conditional on other events P(A/B).

42
Q

What’s the sample space (omega)?

A

The collection of all possible outcomes for an event.

43
Q

What does P(Y given X) means for the value of Omega?

A

X becomes the Omega.

44
Q

What’s the general conditional probability rule?

A

P(B/A)= (P(Band A))/P(A)

45
Q

What is the formula for total probability?

A

P(B)=P(A)P(B/A) + P(not-A)P(B/not-A)

If there are two options, B would be one option and not-B would be the other option.

46
Q

What sum is the total probability equation derived from? How is it converted into the total probability equation?

A

P(A)= P(A and B) + (A and not-B)

This can be converted into the total probability equation by applying the general conjunction rule.

47
Q

In term of dependency, what type of relationship does total probability apply to?

A

To dependent events.

48
Q

What is the Bayes’ Rule formula?

A

P(A/B) = P(A and B)/ P(B)

This formula is expanded to become the working version of Bayes’ rule.

49
Q

When solving Bayesian problems, what information should be organised first?

A

A being one option and B another; and X being the event in question:

P(X/A)
P(X/B)
And the base rates:
P(A) = number of possibilite events/total number (total probability/ prior probability)
P(B) = total probability

Then enter these into the Bayes’ formula.

Logics And Argumentation (6 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions