Lesson 1: Introduction to Probability and Likelihood

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

Outcomes are equally likely when each outcome has the same chance of occurring. The basic probability formula $P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}$ only applies when all outcomes are equally likely.

Examples

Property

Not all outcomes are equally likely just because they exist. Equal probability requires either experimental evidence or knowledge that outcomes have the same chance of occurring. When outcomes are not equally likely, theoretical probability cannot be calculated as $P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$.

Examples