Theoretical Probability

Theoretical probability is the likelihood of an event happening based on all the possible outcomes. It is calculated using the formula:

Probability = Number of favorable outcomes / Total number of possible outcomes

Examples:

Example 1: What is the probability of rolling a 3 on a fair six-sided die?

Number of favorable outcomes = 1 (there is one 3 on the die)

Total number of possible outcomes = 6 (there are six sides on the die)

Probability = 1/6 = 0.1667 or 16.67%

Example 2: What is the probability of drawing a red card from a standard deck of 52 playing cards?

Number of favorable outcomes = 26 (there are 26 red cards in a deck)

Total number of possible outcomes = 52 (there are 52 cards in a deck)

Probability = 26/52 = 0.5 or 50%

Study Guide

1. Understand the concept of theoretical probability and how it is calculated.
2. Practice finding the theoretical probability of simple events using the probability formula.
3. Explore more complex scenarios involving multiple events and calculate the combined theoretical probability.
4. Learn to differentiate between theoretical probability and experimental probability.
5. Apply theoretical probability in real-life scenarios, such as games of chance, sports, and decision-making.

By mastering theoretical probability, you will gain a strong foundation in understanding the likelihood of different outcomes, which is a fundamental concept in mathematics and statistics.