### 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

1 event do not depend on the other

An event A happen given event E already happened

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.

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(A) + P(B)

P(A U B ) = P(E) = 1

4) Independent1 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.