Basic reference for probability that I find myself looking up.
Probability of \(X\):
\[ P(X) \]
When \(X\) and \(Y\) are independent:
\[ P(X \cap Y) = P(X) P(Y) \]
Conditional probability of \(X\) given \(C\):
\[ P(X \mid C) = \frac{P(X \cap C)}{P(C)} \]
Bayes’ theorem:
\[ P(X \mid Y) = \frac{P(Y \mid X) P(X)}{P(Y)} \]