11 - Baye's Theorem Flashcards
(17 cards)
Define an experiment in probability.
A repeatable process which gives rise to a number of outcomes.
Define an event in probability.
A collection (or set) of one or more outcomes.
Define a sample space.
The set of all possible outcomes of an experiment.
What is the range of probability values?
0 to 1
What does a probability of 0 mean?
The outcome is impossible.
What does a probability of 1 mean?
The outcome is certain.
What does P(A) represent?
The probability of event A occurring.
What does P(A’) represent?
The probability of event A not occurring (the complement of A).
What does P (A ∩ B) represent?
The probability of both events A and B occurring (A intersection B).
What does P (A ∪ B) represent?
The probability of either event A or event B or both occurring (A union B).
Write the formula for conditional probability P(B|A).
P(B|A) = P (A ∩ B) / P(A)
Define conditional probability.
The probability that one thing will happen given that another thing has (or has not) happened.
State Bayes’ Theorem (two events).
P(A|B) = [P(B|A) * P(A)] / P(B) = [P(A)P(B|A)] / [P(A)P(B|A) + P(A’) P(B|A’)]
What does “mutually exclusive” mean in probability?
Events that cannot occur at the same time. P (A ∩ B) = 0
If A and B are mutually exclusive, how can you express P (A ∪ B)?
P (A ∪ B) = P(A) + P(B)
What does “independent” mean in probability?
The outcome of one event does not affect the outcome of the other. P (A ∩ B) = P(A) * P(B)
If A and B are independent, how can you express P (A ∪ B)?
P (A ∪ B) = P(A) + P(B) - P(A) * P(B)
