Introduction to Probability

By the end of this lesson, you will be able to calculate basic probabilities, list sample spaces, and interpret probability values.

Probability Scale

Probability ranges from 0 (impossible) to 1 (certain).

$$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}$$

Can be expressed as a fraction, decimal, or percent.

Sample Spaces

The sample space is all possible outcomes. List systematically.

Rolling a die: {1, 2, 3, 4, 5, 6}

Flipping two coins: {HH, HT, TH, TT}

Drawing a card from {A, B, C, D}: {A, B, C, D}

Computing Probabilities

$P(\text{rolling a 3}) = \frac{1}{6}$

$P(\text{rolling even}) = \frac{3}{6} = \frac{1}{2}$ (outcomes: 2, 4, 6)

$P(\text{rolling > 4}) = \frac{2}{6} = \frac{1}{3}$ (outcomes: 5, 6)

Complement: $P(\text{not A}) = 1 - P(A)$

$P(\text{not rolling a 3}) = 1 - \frac{1}{6} = \frac{5}{6}$

Certain and Impossible Events

$P(\text{rolling a number } 1\text{–}6) = \frac{6}{6} = 1$ (certain)

$P(\text{rolling a 7}) = \frac{0}{6} = 0$ (impossible)

Summary

Probability = favorable ÷ total outcomes; always between 0 and 1.

Sample space: list ALL possible outcomes.

Complement rule: $P(\text{not A}) = 1 - P(A)$.