Section 15.2: Probability

Property

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around $\frac{1}{2}$ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. If $A$ is any event and $S$ is the sample space, then $0 \leq P(A) \leq 1$.

Examples

• The probability of a standard six-sided die landing on the number 9 is 0. This is an impossible event.
• The probability that an object dropped will fall down is 1. This is a certain event.
• When drawing a card from a standard 52-card deck, the probability of drawing a black card is $\frac{26}{52} = \frac{1}{2}$, an event that is equally likely as not.

Explanation

Probability is measured on a scale from 0 to 1. A probability of 0 means an event is impossible. A probability of 1 means it's certain. A probability of $\frac{1}{2}$ means it's equally likely to happen or not happen.

Property

When all outcomes in a sample space are equally likely, the theoretical probability of an event is:

Examples

Property

A uniform probability model assigns equal probability to all outcomes in the sample space. In a uniform model, if there are $n$ equally likely outcomes, then each outcome has probability $\frac{1}{n}$.

The probability of any event is calculated as: