Probability
A numerical measure of the likelihood that an event will occur, bounded between 0 and 1.
The exam loves to hand you the general addition rule, P(A or B) = P(A) + P(B) − P(A and B), then trick you with non-mutually-exclusive events where students forget to subtract the overlap and overstate the union. Watch for the total probability rule, where an unconditional P(A) is rebuilt by weighting conditional probabilities across mutually exclusive, exhaustive scenarios — that setup is almost always the lead-in to a Bayes’ update. Another staple is converting between probabilities and odds: odds for an event equal P/(1 − P), odds against are the reciprocal (1 − P)/P, and a common slip is reporting one when the item asks for the other.
A deeper trap is treating independence and mutual exclusivity as near-equivalent when they are nearly opposites: two events with positive probability that are mutually exclusive cannot be independent, since one occurring forces the other’s probability to zero. Distinguish probability from sampling — probability assumes the model is known and computes outcome likelihoods, whereas sampling estimates unknown parameters from data — and from regression, which fits a relationship between variables rather than quantifying uncertainty.
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