To quantify how likely the possible outcomes are
Explication
Probability is used to quantify the likelihood of outcomes produced by a random experiment. It does not remove randomness or make the outcome exactly predictable.
It restricts the universe to the cases where the condition is true
Explication
Conditional probability is computed after adding extra information, so the reference universe is restricted to the subset where the condition holds. The full sample space is not used unchanged.
By dividing the row or column total by the overall total
Explication
A marginal frequency is the proportion of the whole population having a given value, so its denominator is the overall total. Dividing by a row or column total gives a conditional frequency instead.
The proportion of b1 among individuals already having a1
Explication
Conditional frequency measures how common b1 is inside the subpopulation defined by a1. Its denominator is the marginal count for a1, not the total population.
A procedure whose outcome cannot be predicted in advance
Explication
A random experiment is a procedure with an outcome that cannot be predicted beforehand. A single possible result describes an elementary event, not the experiment itself.
An event containing exactly one possible outcome
Explication
An elementary event contains exactly one outcome from the universe. The complete set of all outcomes is the universe Ω, not an elementary event.
P(A ∩ B) divided by P(B)
Explication
Conditional probability is defined by P_B(A)=P(A∩B)/P(B) when P(B)≠0. This reflects restricting attention to the cases where B occurs.
The probability of A inside the universe where B is known to occur
Explication
P_B(A) means the probability of A given that B has occurred, so the universe is restricted to B. It is not the unrestricted probability of A.
The product of the branch probabilities along that path
Explication
In a weighted tree, the probability of a path is obtained by multiplying the branch probabilities along that path. Adding branch probabilities is used only for branches leaving the same node.
They must add up to 1
Explication
Branches leaving the same node represent all possible next choices from that condition, so their probabilities sum to 1. Equal branch probabilities are not required.
P(A)=P(A∩B)+P(A∩B̄)
Explication
The total probability formula writes A as the union of two disjoint cases: through B and through B̄. Since the cases do not overlap, their probabilities add.
It helps recover a missing probability using the total probability relation
Explication
Tree inversion is used when a needed probability is not directly shown in the original tree, and the total probability relation helps recover it. It does not create independence or eliminate conditioning.
When knowing one does not change the probability of the other
Explication
Independence means that learning one event occurred does not change the probability of the other. If the events cannot occur together, that is mutual exclusivity, not independence.
P(A) × P(B)
Explication
For independent events, the product rule gives P(A∩B)=P(A)×P(B). This is equivalent to saying the conditional probability equals the unconditional probability.
Mémorisez les réponses avec 14 flashcards sur Fundamentals of Probability and Independence.
Probability — purpose?
Quantify likelihood of outcomes.
Contingency table — frequencies?
Counts or proportions of characteristics.
Experiments and events — vocab?
Experiments produce outcomes; events are outcome sets.
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