Empirical Probability Study Guide

Definition:

Empirical probability is the probability of an event based on actual data or observations. It is calculated by taking the number of favorable outcomes and dividing it by the total number of outcomes.

Formula:

The formula for empirical probability is:

Empirical Probability = Number of Favorable Outcomes / Total Number of Outcomes

Example:

Suppose you roll a fair six-sided die and want to find the empirical probability of rolling a 3. You roll the die 50 times and get 10 3s. The empirical probability of rolling a 3 is:

Empirical Probability of rolling a 3 = 10 / 50 = 0.20

Steps to Calculate Empirical Probability:

Identify the event for which you want to find the empirical probability.
Conduct the experiment and collect data on the number of favorable outcomes.
Divide the number of favorable outcomes by the total number of outcomes to calculate the empirical probability.

Properties:

Empirical probability is based on actual data and can vary depending on the sample size and the specific outcomes observed.

Use Cases:

Empirical probability is often used in fields such as statistics, economics, and sports to make predictions based on observed data.

◂Math Worksheets and Study Guides Sixth Grade. Ratio

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Grade 6 Curriculum Focal Points (NCTM)

Number and Operations: Connecting ratio and rate to multiplication and division

Students use simple reasoning about multiplication and division to solve ratio and rate problems (e.g., 'If 5 items cost $3.75 and all items are the same price, then I can find the cost of 12 items by first dividing $3.75 by 5 to find out how much one item costs and then multiplying the cost of a single item by 12'). By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative sizes of quantities, students extend whole number multiplication and division to ratios and rates. Thus, they expand the repertoire of problems that they can solve by using multiplication and division, and they build on their understanding of fractions to understand ratios. Students solve a wide variety of problems involving ratios and rates.