Probability Events in
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Compound
events
In case of easy events we consider the probability of the happening or not
happening of solo events. For instance, we might be interested in judging out
the probability of drawing a red ball from a bag holding to white and 6 red
balls. Conversely, In case of compound events we consider the connect
occurrence of two or more happenings.
Exhaustive events
Events are supposed to be exhaustive when their entirety includes all the
possible results of a random experiment.
Complementary events
let there be two occasions A and B. A
is known as the complementary event of B (and vice versa), if A and B are equally
exclusive and exhaustive. For instance, when a dice is thrown, happening of an
even number (2, 4, 6,) and odd number (1, 3, 5,) are complementary
events.
Concurrent occurrence of two events A and B is commonly written as Ab.
Theorems of probability
there are two significant theorems of probability, namely:
·
The addition theorem
·
The multiplication theorem
Addition theorem
The addition theorem says that if two events A and B are mutually exclusive the
probability of A and B. emblematically,
p (A or B) = p (A) + P (B).
Prof of the theorem, if an event A can occur as two methods a1 methods and B in
a2 methods. Then the number of methods in which either event can occur is a1 + a2.
If the total number of possibilities is n, then by meaning the probability if
either the first or the second event occurring is
a1 + a2/N = a1/n
+ a2/n
But, a1/n = p (A)
And, a2/n = p (B)
therefore, p (A or B) = P (A) + P (B).
Multiplication theorem
this theorem says that if two occurrences A and B are self-regulating, the
prod, capability that they both will happen is equal to the product of their
individual probability. emblematically, it A and B ate independent, then
P (A and B) = p (A) A x P (B)
P (A, B and C) = P (A) x p (B) x P (C)
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