# Probability Addition Theorem

**1. When events are mutually exclusive**

P(A or B) = Probability of A + Probability of B

For example, you have a coin and you have tossed. You have estimated whether head or tail comes. At that time, happening of head does not effect the happening of tail or vise-versa. So, if we have to calculate the happening of A or b, it will be equal to the total of the probability of A and probability of B.

**2. When events are not mutually exclusive.**

Probability of (A or B) = P(A) + P(B) - P(AB)

When the events are not mutually exclusive, it means, there will be some common event which is happening both in A and B, so, we will deduct the probability of multiplication of A and B from the total of p(A) and P(B).

For example, we have to calculate the probability of a king or a black card. At that time, we will calculate the probability of king 4/52, probability of back 26/52.We know that there are 2 common card which are black and king. So probability of (King and Black card) will be 2/52

**P(K or B) = 4/52 + 26/52 - 2/52 = 7/ 13 = 53%**

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