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

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

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

Example: Blue Cards

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

\(P(blue)=\frac{0}{52}=0\)

Example: Rolling a Value Between 1 and 6

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.

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