Hey Developer’s, I’m back with a new topic which is Multiplicative and Additive Law Of Probability in the series of statistics foundations.

### Quick Refresher

If any of the following condition holds, then the two events A and B are independent,

- P(A|B) = P(A)
- P(B|A) = P(B)
- P(A∩B) = P(A)P(B)

If none of these condition holds, the events are **dependent** and if any one of the condition holds from this the events are **independent**.

So, let’s get started …

### Multiplicative Law Of Probability

As we learned before the formula of conditional probability,

P(A|B) = P(A∩B) / P(B)

The probability of intersection of two events A and B is

P(A∩B) = P(B)P(A|B) = P(A)P(B|A),if values swapped

If these events are independent, then P(A∩B) = P(A)P(B)

### Multiplicative Law Examples

**Two Dependent Events:**

- A – Odd Number
- B – number < 4

P(A) = 1/2 ; P(B) = 1/2

P(A|B) = 2/3; P(B|A) = 2/3

Explanation: Only two odd numbers out of nmber < 4 means 3 values {1,2,3}. so 2/3.

P(A∩B) = P(A)P(B|A) = 1/2 * 2/3 = 1/3

### Additive Law Of Probability

Probability of a union of events, P(A U B) = P(A) + P(B) – P(A∩B)

If A and B are mutually exclusive,P(A∩B) = 0 and

P(A U B) = P(A) + P(B)

We can extend this formula to calculate the probabilities of more than 2 events.

#### Next Post will be on Laws Of Total Probability

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