Find the Probability of an Event | The Center for Quantitative Studies | Studio Aletheia
The Center for Quantitative Studies spinning orb Studio Aletheia · The Center for Quantitative Studies 6.DPSR.2.2SC 6th Grade Math

Find the Probability of an Event

Lesson 18 · New Content, Find the Probability of Simple Events

You already know how to describe an event as likely or unlikely — today you'll go further and calculate exactly how likely, as a single number. That number is called a probability, and it's the same idea whether you write it as a fraction, a decimal, or a percent.

Focus Calculating Probability
Accountability Data Journal + Exit Ticket
Indicator Find the probability of a simple event as a fraction, decimal, or...
The Center for Quantitative Studies Color Palette Aletheian Green · Aletheian Gold
Learning Targets

Learning Targets and Success Criteria

Today you'll turn likelihood language into an exact probability value.

Targets

What I will learn

  • I can identify the favorable outcomes and total outcomes for a simple event.
  • I can calculate the probability of a simple event as a fraction.
  • I can convert a probability fraction into a decimal and a percent.
  • I can explain what a probability value means in the context of an event.
Success Criteria

What success looks like

  • I can write a probability as favorable outcomes over total outcomes in lowest terms.
  • I can convert at least three probability fractions to decimals and percents accurately.
  • I can explain, in a sentence, what a probability of 1/4 means for a real event.
  • I can check that my probability value makes sense given the likelihood word for the event.
Standard 6.DPSR.2.2

Calculate the probability of a simple event as a fraction, decimal, or percent.

6.DPSR.2.2 — Find the probability of a simple event (a single outcome or a small favorable set) as a fraction, decimal, or percent, expressed as favorable outcomes over total outcomes.
Vocabulary

The words we'll use in today's lesson.

These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.

01 · Calculate

Probability

A number from 0 to 1 (or 0% to 100%) that tells how likely an event is to happen, found as favorable outcomes over total outcomes.

02 · Identify

Simple Event

An event made up of a single outcome, or a small set of favorable outcomes, from all the possible outcomes in a situation.

College & Career Connections

Where this shows up in the real world.

Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.

Actuary / Insurance Analyst

Turning Likelihood Into a Number

The likelihood words from last week are just the beginning — actuaries need an exact number to set a fair price. Soon you'll see how the probability calculations you learn today are the very same math actuaries run every day, just with far bigger data sets.

Mini-Lesson

From Words to Numbers

Today you'll turn likelihood language into an exact probability value.

A simple eventAn event made up of a single outcome, or a small set of favorable outcomes, from all the possible outcomes in a situation. is any single outcome, or small group of outcomes, you're interested in out of everything that could happen. Rolling a 3 on a number cube is a simple event. So is pulling a red marble from a bag, or landing on a striped section of a spinner. Once you can name the favorable outcomes and the total outcomes for a simple event, you're ready to calculate exactly how likely it is.

That exact number is called probabilityA number from 0 to 1 (or 0% to 100%) that tells how likely an event is to happen, found as favorable outcomes over total outcomes., and it is always found the same way: favorable outcomes over total outcomes. If a spinner has 8 equal sections and 2 are yellow, the probability of landing on yellow is 2/8, which simplifies to 1/4. That same probability can be written as the decimal 0.25 or the percent 25%, three different outfits for the exact same idea, just like Lesson 1 taught you fractions, decimals, and percents always are. A probability of 1/4 tells you the event is unlikely, since it's less than 1/2, which lines up perfectly with the likelihood words you already know.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.

Check for Understanding · CFU 1
A bag has 20 marbles: 5 red and 15 blue. What is the probability of pulling a red marble? Write your answer as a fraction, a decimal, and a percent.
Toolkit

Materials for the Data Lab.

  • A. A number cube (1-6)
  • B. A spinner divided into 8 equal sections
  • C. A bag of 10 or 20 marbles
  • D. Your Data Journal
  • E. A calculator (optional)
Non-negotiable routine

Always write a probability as favorable-over-total first, then simplify, then convert to a decimal and a percent.

Guided Practice

Probability Lab

Today's lab has you calculate real probability values from small, simple data sets.

Data Lab
Each scenario below has outcome counts chosen so your fractions simplify cleanly — calculate the probability for each.
1 · Identify
Identify the favorable outcomes and total outcomes for each scenario.
2 · Calculate
Calculate the probability of each event as a fraction in lowest terms.
3 · Convert
Convert each fraction probability into a decimal and a percent.
4 · Explain
Explain what your probability value tells you about how likely the event is.
Hands-On

Calculate and Convert

You'll calculate probabilities from today's scenarios and represent each one three ways.

1
Count: Count the favorable outcomes and total outcomes for each scenario.
2
Calculate: Calculate the probability of each event as a simplified fraction.
3
Convert: Convert each fraction into a decimal and a percent.
4
Check: Check that your probability value matches the likelihood word you'd expect.
Required

Data Journal Entry

Which Mathematical Process Standard did you rely on most today — Problem Solving, Connections, Representation & Communication, Analyze & Justify, or Structure & Patterns? Give one specific example from your Data Lab or hands-on work.
Checklist

Accountability Checklist

Required · Exit Challenge

What's the Probability?

A spinner has 5 equal sections: 1 orange, 4 teal. Find the probability of landing on orange as a fraction, decimal, and percent.

Lesson 18 · New Content, Find the Probability of Simple Events

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