# Probability Properties

### Probability Axioms

1.The probability is positive and less than or equal to 1.

**0 ≤ p(A) ≤ 1**

2. The probability of the sure event is 1.

**p(S) = 1**

3.If A and B are mutually exclusive, then:

**p(A B) = p(A) + p(B)**

### Probability Properties

1 The sum of the probabilities of an event and its complementary is 1, so the probability of the complementary event is:

2 The probability of an impossible event is zero.

3 The probability of the union of two events is the sum of their probabilities minus the probability of their intersection.

4 If an event is a subset of another event, its probability is less than or equal to it.

5 If A_{1}, A_{2}, ..., A_{k} are mutually exclusive between them, then:

6 If the sample space **S** is finite and an event is S = {x_{1}, x_{2}, ..., x_{n}} then:

For example, the probability of obtaining an even number, when rolling a die, is:

P(even) = P(2) + P(4) + P(6)