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1. Permutation

^{n}P_{r} =

2. Combination

^{n}C_{r} =

3. Defination of Probability

P(E) =

Number of outcomes favourable to E

Number of all possible outcomes

4. Complementary events

If B and A are complementary events then P(B) = P(A') = 1 - P(A)

5. Addition Theorem of Probability

If A and B are two events of sample space S, then

P(A È B) = P(A) + P(B) - P(AÇ B)

If A and B are mutually exclusive events then P(A È B) = P(A) + P(B)

If A and B are any two events of sample space S, then

P(A) = P(A Ç B) + P(A Ç B')

6. Conditional Probability

P(A/B) is read as 'Probability of A when B has taken place' or 'Probability of A under B'

\ P(A/B) =

P(A Ç B)

, where P(A) ¹ 0

P(A)

7. Multiplication Theorem of Probability

If A and B are any two events such that P(A) ¹ 0, then

P(A Ç B) = P (A) · P

Similarly, if P(B) ¹ 0 then

P(A Ç B) = P (B) · P

8. Independent Events

Events A and B are said to be independent events if P(A/B) = P(A) OR P(B/A) = P(B)

If A and B are two independent events such that P(A) ¹ 0, P(B) ¹ 0, then

P(A Ç B) = P (A) . P(B)

If A and B are independent events such that P(A) ¹ 0, P(B) ¹ 0, then

P(A Ç B') = P (A) . P(B')