Question

What are the two basic laws of probability?

Answer 1

Hint: Here, we are asked to explain the two basic laws of probability. We generally apply probability to deal with the occurrence of a random event and the required always lies between $0$ to $1$
Also, there are two basic laws of probability; they are the addition rule and the multiplication rule.

Complete step by step answer:
Generally, in mathematics, we apply probability to deal with the occurrence of a random event and the required always lies between $0$ to $1$ (but not equal to$1$ )
There are two basic laws of probability which are as follows.
Addition rule.
Multiplication rule.
1) Addition rule
If $A$ and $B$ are the respective random events defined on a sample space, then we have
$P(AorB) = P(A) + P(B) - P(AandB)$ ….$\left( 1 \right)$
Suppose $A$ and $B$ are mutually exclusive events, then$P(AandB) = 0$ .
Thus, the equation $\left( 1 \right)$ becomes$P(AorB) = P(A) + P(B)$ (The two events are said to be mutually exclusive if they cannot occur at the same time (i.e.) mutually exclusive means disjoint.)
2) Multiplication rule:
If $A$ and $B$ are the respective random events defined on a sample space, then we have
$P(A\& B) = P\left( {\dfrac{A}{B}} \right) \times P(B)$ …..$\left( 2 \right)$
Suppose $A$ and $B$ are independent events, then we have
$P\left( {\dfrac{A}{B}} \right) = P\left( A \right)$ (Two events are said to be independent if the occurrence of an event does not affect the probability of occurrence of the other event.)
We shall substitute the above result in the equation$\left( 2 \right)$ thus, we get $P(A\& B) = P(A) \times P(B)$

Note: Generally, two events are said to be mutually exclusive if they cannot occur at the same time (i.e.) mutually exclusive means disjoint.
And two events are said to be independent if the occurrence of an event does not affect the probability of occurrence of the other event.
Hence, the two basic laws of probability are the addition rule and the multiplication rule.