Casework and Law of Total Probability

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

$P(A/B)=P(A)$

$P(A^C)= 1-P(A)$

$P(A)=P(A|B_1)P(B_1)+P(A|B_2)P(B_2)+...+P(A|B_k)P(B_k)$