+ P ( B ) (ii) The addition theorem may be extended to any three events A,B,C and we have P A P A P B P C P A ∪ ∪ ∩ ) = ) + ( ) − ( P A P B ∩ ∩ − ( ) − ( ) + ( P A It is believed that the students might be familiar with the above concepts and our present syllabus continues from the following. . . Independent and Dependent events (i) Independent Events Two or more events are said to be independent when the outcome of one does not affect and is not affected by, the other.
For example, if a coin is tossed twice, the result of the second throw would in no way be affected by the result of the first throw. (ii) Dependent events Are those in which the occurrence or non- occurrence of one event in any one trial affects the other events in other trials. For example the probability of drawing a queen from a pack of cards is or . But if the card drawn (queen) is not replaced in the pack, the probability of drawing again a queen is .
. . Conditional Probability If two events A and B are dependent, then the conditional probability of B given that A as occurred already is P ( B / A ) = P A P A ( ) ; P ( A ) ≠ Similarly P ( A / B ) = P A P B ( ) ; P ( B ) ≠ - - Descriptive statistics and probability (i) Multiplication Theorem: The probability of the simultaneous happening of two events A and B is given by P ( A ∩ B ) = P ( A ). P ( B / A ) (or) P ( A ∩ B ) = P ( B ).
P ( A / B ) NOTE If A and B are two independent events then P (