Let E, F and G are three events of sample space S then
Thus, the multiplication rule of probability can be extended for four or more events.
Independent Events:
If A and B are two events such that the probability of occurrence of one of them is not affected by occur¬rence of the other. Such events are called independent events.
Two events A and B are said to be independent, if =P(A), provided P(B) * 0
P \((\frac{A}{B})\) = P(A), provided P(B) ≠ 0
and P \((\frac{B}{A})\) = P(B), provided P(A) ≠ 0
By multiplication theorem of probability
P \((\frac{A}{B})\) = P(A)P \((\frac{B}{A})\)
If A and B are independent events, then
P(A ∩ B) = P(A) P(B)
Note : Three events A, B and C are said to be mutually independent if
P(A ∩ B)=P(A). P(B)
P(B ∩ C) =P(B). P(C)
P(A ∩ C) = P(A). P(C)
and P(A ∩ B ∩ C) = P(A). P(B). P(C)
If at least one of the above is not true for three events, we say that the events are not independent.
