Week 6/7 - Probability

classical definition of probability

-probability of event = outcomes with event/total number of outcomes
-assumes all events are equally likely

frequentist definition of probability

-probability of event = observations/total observations
-repeats similar experiment

subjective definition of probability

P(A ∪ B) =

P(A) + P(B) - P(A ∩ B)

P(A ∩ B) =

P(B | A)*P(A)

P(A | B) =

(P(A ∩ B) / P(B))

Bayes’ theorem

conditional probability: P(A|B) = (P(A ∩ B) / P(B))

P(A ∪ B) meaning

The probability that either event A or B (or both) happen

P(A ∩ B) meaning

The probability that both events A and B happen

P(A | B) meaning

The probability that A happens assuming that B happened

standard normal distribution