A bit on probability

The addition rule of probability says that the probability of occurrence of atleast one of the two events A and B is given by:

P(AÈB) = P(A) + P(B) – P(AÇB)

The multiplication rule of probability says that the probability of simultaneous happening of two events A and B is given by:

P(AÇB) = P(A). P(A|B) ; P(A) ¹ 0    or,

P(BÇA) = P(B). P(B|A)  ; P(B) ¹ 0

where P(B|A) is the conditional probability of happening of B under the condition that A has happened and P(A|B) is the conditional probability of happening of A under the condition that B has happened.

Thus, the addition rule gives the probability of happening of at least one event out of all the possible events while the multiplication rule gives the probability of happening of all the events simultaneously.

Independence: Events are said to be independent of each other if happening of any one of them is not affected by and does not affect the happening of any one of the others.

If A and B are independent events, then:

P(A|B) = P(A)   and P(B|A) = P(B)

Two events are dependent if the above does not hold.

Multiplication rule for independent events thus becomes:

P(AÇB) = P(A).P(B)