Conditional Probability and Independence (VCE SSCE Mathematical Methods): Flashcards

Prob. of event A when event B has already occurred

The probability of $A$ given $B$

$\text{Pr}(A \mid B) = \frac{\text{Pr}(A \cap B)}{\text{Pr}(B)}$

$\text{Pr}(A \cap B) = \text{Pr}(A \mid B) \times \text{Pr}(B)$

One event occurring doesn't change prob. of the other

$\text{Pr}(A \cap B) = \text{Pr}(A) \times \text{Pr}(B)$

$\text{Pr}(A)$ summed over all partitions of $B$

Multiply probabilities along the branches

$\text{Pr}(A)$

Calculate directly from relevant rows/columns