Education Technology

# Statistics and Probability / Law of Large Numbers

Grade Level 6,7
Activity 16 of 24
In this lesson, students investigate how the relative frequency of an outcome approaches the actual probability of that outcome, as the number of repetitions gets larger and larger (the law of large numbers).

## Planning and Resources

Objectives
Students recognize that the relative frequency of an outcome is likely to be close to the actual probability of that outcome as the number of repetitions gets larger and larger (the law of large numbers). They can estimate the probabilities of possible outcomes by repeating the chance process a large number of times.

Vocabulary
distribution
variability
sample space
outcome
frequency
relative frequency

Standard:

## Lesson Snapshot

#### Understanding

The frequency is just the count for how many times a color was drawn. The relative frequency is how many times a certain color jellybean occurred divided by the total number of jellybeans drawn.

### What to look for

Students recognize that the relative frequency of an outcome is likely to be close to the actual probability of that outcome as the number of repetitions gets larger and larger (the law of large numbers).

### Sample Assessment

If you knew the sample space consisted of four outcomes, which of the following is true?

a. The probability of each outcome is 0.25.
Answer: False

b. The sum of the probabilities of each outcome is 1.
Answer: True

c. None of the probabilities of the outcomes is
greater than 0.5.
Answer: False

d. The probability of one outcome is 0.25.
Answer: False

#### The Big Idea

Over the long run, the relative frequencies of outcomes of chance processes stabilize as the sample size gets larger and can be used to estimate probabilities.

### What are the students doing?

Students repeat an experiment a large number of times to explore the relationship between the relative frequency and the actual probability for an outcome.

### What is the teacher doing?

Be sure students note that the distributions of results will often vary greatly when only a small number of samples is taken.