May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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Combinatorics 5-29
Definition 5.2 Two events A and B are said to be independent if the probability of each
is unaffected whether the other happens or not. Thus, events A and B are independent if
þ(A/B) = þ(A) and þ(B/A) = þ(B).
5.10 MULTIPLICATION THEOREM INDEPENDENT EVENTS
Multiplying equation (5.4) by þ(B) ≠ 0, we have
þ(B ∩ A) = þ(A ∩ B) = þ(B) þ(A/B) (5.5)
as events A ∩ B and B ∩ A are equivalent, we can also write
þ(A ∩ B) = þ(A) þ(B/A) (5.6)
That is, if in an experiment, the events A and B can both occur, then
þ(A ∩ B) = þ(A) þ(B/A)
This is known as multiplication theorem. If the events A and B are independent,
þ(A ∩ B) = þ(A) þ(B) (5.7) ...
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