Revise: Probability
Sample spaces and the probability formula, the complement rule, the addition and multiplication rules for combined events, conditional probability, and expected frequency.
P(E) = n(E)/n(S), when outcomes are equally likely.
P(even, 1 die) = 3/6 = 1/2.
Independent events: P(A∩B) = P(A)×P(B).
P(2 heads) = 1/2×1/2 = 1/4.
P(E) = n(E)/n(S). Sample space = all outcomes; event = a chosen subset.
P(red ball, 4 of 10) = 0.4.
P(E') = 1 − P(E) — useful when the opposite is easier to find.
3 coins: P(≥1 head) = 1 − 1/8 = 7/8.
P(A∪B) = P(A)+P(B)−P(A∩B); mutually exclusive drops the overlap term.
Mutually exclusive: P(A)=0.5, P(B)=0.3 → P(A∪B)=0.8.
Independent: outcome of one does not affect the other. P(A∩B)=P(A)P(B).
Coin + die: P(heads and 6) = 1/12.
P(A|B) = P(A∩B)/P(B) — probability of A within the reduced sample space B.
P(king|face card) = 1/3.