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.
Learning Targets and Success Criteria
Today you'll turn likelihood language into an exact probability value.
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.
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.
Calculate the probability of a simple event as a fraction, decimal, or percent.
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.
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.
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.
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.
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.
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.
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)
Always write a probability as favorable-over-total first, then simplify, then convert to a decimal and a percent.
Probability Lab
Today's lab has you calculate real probability values from small, simple data sets.
Calculate and Convert
You'll calculate probabilities from today's scenarios and represent each one three ways.
Data Journal Entry
Accountability Checklist
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.
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