Identify the sample space (all possible outcomes)
Identify the event of interest (subset of outcomes)
Choose the probability model
For equally likely outcomes: compute (P(E)=frac{|E|}{|S|})
For counting with combinations: compute (P(E)=frac{text{number of favorable outcomes}}{text{number of total outcomes}})
For empirical probability (from data): compute (P(E)approx frac{text{count of times }Etext{ occurs}}{text{total trials}})
For independent events: use (P(Acap B)=P(A),P(B))
For independent events (complement): use (P(A^c)=1-P(A))
For mutually exclusive events: use (P(Acup B)=P(A)+P(B))
In general (addition rule): use (P(Acup B)=P(A)+P(B)-P(Acap B))
For complements: use (P(E)=1-P(E^c))
For conditional probability: compute (P(Amid B)=frac{P(Acap B)}{P(B)}) (when (P(B)>0))
For conditional probability (rule of multiplication): use (P(Acap B)=P(B),P(Amid B))
For counting permutations: use (nPr=frac{n!}{(n-r)!})
For counting combinations: use (nCr=frac{n!}{r!(n-r)!})
For binomial probabilities: (P(X=k)=binom{n}{k}p^k(1-p)^{n-k})
For binomial cumulative probabilities: sum binomial terms for the required range of (k)
For normal probabilities: standardize with (z=frac{x-mu}{sigma}) and use the normal CDF
For continuous distributions: use (P(ale Xle b)=int_a^b f(x),dx)