# 2.1.3.1 - Range of Probabilities

The probability of an impossible event is 0 and the probability of a certain event is 1. The range of possible probabilities is: $$0 \leq P(A) \leq 1$$. It is not possible to have a probability less than 0 or greater than 1.

## Example: Rolling an 8 Section

It is impossible to roll an eight on a six-sided die.

$$P(rolling\; 8)= \dfrac{0}{6} = 0$$

## Example: Blue Cards Section

In a standard 52-card deck all cards are black or red. There are no blue cards.

$$P(blue)=\dfrac{0}{52}=0$$

## Example: Rolling a Value Between 1 and 6 Section

A six-sided die contains the values 1, 2, 3, 4, 5, and 6. All rolls will result in a value between 1 and 6.

$$P(rolling \;1 \;to\; 6)=\dfrac{6}{6}=1.00$$