Further Probability (A Level only) (AQA A-Level Mathematics): Flashcards

$P(A) = \frac{\text{Favourable}}{\text{Total}}$

$P(A') = 1 - P(A)$

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$P(A \cap B) = P(A) \times P(B)$

$P(A \cap B) = P(A) \times P(B \mid A)$

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

Probability of $B$ given $A$ has occurred

$P(A) = \sum P(B_i) \times P(A \mid B_i)$

$P(B_i \mid A) = \frac{P(B_i) \times P(A \mid B_i)}{P(A)}$

$P(\text{At least one}) = 1 - P(\text{None})$