Question

What are the two laws of probability?

Answer 1

Laws of Probability:

Probability is the chance of occurrence of an event.

The two laws of probability are:

• Addition rule
• Multiplication rule

Addition rule:

If $A$and $B$are mutually inclusive events i.e., both can occur simultaneously, the addition rule is

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

If $A$and $B$are mutually exclusive events i.e., both cannot occur simultaneously, the addition rule is

$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)$

Multiplication rule:

If $A$and $B$are dependent events, the multiplication rule is

$P\left(A\cap B\right)=P\left(A\right)·P\left(B|A\right)$ or $P\left(A\cap B\right)=P\left(B\right)·P\left(A|B\right)$

If $A$and $B$are independent events, the multiplication rule is

$P\left(A\cap B\right)=P\left(A\right)·P\left(B\right)$