Question

What are the two basic laws of probability?

Answer 1

The two basic laws of probability are as follows:

If $A$ and $B$ are two events defined on a sample space

• Addition rule: When $A$ and $B$ are not mutually exclusive: $P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$. Special case: When $A$ and $B$ are mutually exclusive, we get $P\left(AandB\right)=0$. Then, $P\left(AorB\right)=P\left(A\right)+P\left(B\right)$

• Multiplication rule: When $A$ and $B$ are not independent: $P\left(AandB\right)=P\left(B\right)P\left(A|B\right)$. Special case: When $A$ and $B$ are independent, we get $P\left(A|B\right)=P\left(A\right)$. Then, $P\left(AandB\right)=P\left(A\right)P\left(B\right)$