Mutually Exclusive Events and Independent Events:

"Two events are said to be Mutually exclusive even "ts with respect to each other if occurrence of one excludes the occurrence of the other "

- For example : If two men, say M1 and M2 proposed the same lady W for marriage and A and B are two events defined as follows : A =" M1gets married to W" and B="M2 gets married to W"

- Now from the example mentioned above it is quite clear that the events A and B can not happen at the same time,i.e., occurrence of event A excludes the occurrence of event B and vice versa so we can say that the events A and B are two mutually exclusive events.
- On the other hand two events are said to be Independent Events if occurrence of one event does not affect the occurrence of the other.
- For example if a man M1 proposed to a woman W1 and a man M2 proposed to another woman W2. Now in this case if A and B are events such that A = "M1 gets married to W1" and B ="M2 gets married to W2", clearly the events A and B do not affect each other in any way. Thus here in this case the events A and B are Independent Events.
- Addition Theorem of Probabilities: If A and B are two mutually exclusiveevents, then Probability ( A ? B) = Probability (A) + Probability (B)

- It may also be written as P(A ? B) =P(A) +P(B) or P(A or B) = P(A) + P(B)

Multiplication Theorem of Probabities:

"If A and B are two independent events, then P(A ∩ B) = P(A).P(B)

or P(A and B) = P(A) . P(B) "