Quick Recap — Probability Basics

  • 0P(A)10\le P(A)\le1; P(sure)=1P(\text{sure})=1, P(impossible)=0P(\text{impossible})=0, P(A)=1P(A)P(A')=1-P(A).
  • Addition: P(AB)=P(A)+P(B)P(AB)P(A\cup B)=P(A)+P(B)-P(A\cap B); mutually exclusive P(AB)=0\Rightarrow P(A\cap B)=0.
  • Independent: P(AB)=P(A)P(B)P(A\cap B)=P(A)P(B).
  • Sample-space sizes: coin 22, die 66, two dice 3636, deck 5252.