Probability


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Probability


Important Points :

Definition : The extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.

1) Equally likely
P(A) = P(B)
2) Mutually exclusive
P(A) ∩ P(B) = ∅
P(A U B) = P(A) + P(B)
3) Collectively Exhaustive<
P(A U B ) = P(E) = 1
4) Independent
1 event do not depend on the other
P(A) ∩ P(B) = P(A) * P(B)
5) Multually exclusive & Collectively Exhaustive
P(A) + P(B) = 1
6) Conditional probability
An event A happen given event E already happened
P(A)/P(E) = P(A ∩ E) / P(E) => If they are dependent
P(A/E) = P(A ∩ E)/P(E) = P(A) => If they are independent
7) Pigeon hole principle
the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.
N=k *(r-1)+1 where k is the number of possible outcomes and r is the number of repetitions we want.