Probability and Uncertainty Flashcards
Probability let’s us quantify _______.
uncertainty
Experiment: rolling a die
Sample space:
Event:
Sample space: 1,2,3,4,5,6
Event: even (2,4,6)
What is a hit?
The occurrence of an event
T or F
Probability can be any number.
False, probability is between 0 and 1.
Mutually exclusive probabilities add up to _______.
1
Classical approach
possible outcomes for E / total possible outcomes
Relative frequency approach
of trials where E occurs / total # of trials
Subjective approach
based on best guess, should be guided by existing information/research
When do we use the subjective approach?
When trials are not possible
Unions
A or B
disjunctions
Intersections
A and B
conjunctions
Marginal vs. Joint probability
marginal: simple
joint: 2+ variables
Conditional probability
Probability of _______ based on _______.
Independent events
the occurrence of one does not predict the occurrence of another
Race and sex are independent events.
What is P(Female|Black)?
P(Female|Black) = P(Female)
Dependent events
the occurrence of one helps predict the occurrence of another
Gender and political party are dependent events in the House of Representatives.
T or F
P(Female|Democrat) = P(Female)
False, this would be true if they were independent.
What is the probability rule for the conjunction of two independent events?
P(A and B) = P(A) x P(B)
What is the probability rule for the conjunction of two dependent events?
P(A and B) = P(A) x P(B|A) = P(B) x P(A|B)
Does rolling a six on two dice at once represent independent or dependent events?
Independent
Does drawing two spades from a deck of cards without replacing cards represent independent or dependent events?
Dependent
What are two cautions in testing for independence?
- Testing whether P(A|B) = P(B|A) does not test independence
- You cannot assume independence
T or F
P(A|B) = P(B|A)
False, for example, all pregnant people have a uterus but not all people with a uterus are pregnant.
T or F
P(A|B) = P(B|A) when P(A) = P(B)
True
Random variable
variable whose value is a numerical outcome of a random process
The mean of X is sometimes called the _______ of X or the _______ of X, written as _______.
expected value, expectation, E(X)
