Studio Aletheia · The Center for Quantitative Studies
6.DPSR.2.1SC 6th Grade Math
State the Likelihood of an Event
Lesson 15 · New Content, State the Likelihood of an Event
Every event in life sits somewhere between impossible and certain, and mathematicians have precise words for exactly where. Today you'll learn to describe how likely an event is using five specific terms, and start connecting that everyday language to an actual probability value.
Learning Targets and Success Criteria
Every event you can imagine has a spot on a single scale, and today you'll learn to name that spot precisely.
What I will learn
- I can describe an event as certain, likely, unlikely, impossible, or equally likely.
- I can place an event on a likelihood scale that runs from impossible to certain.
- I can explain why an event is more or less likely by looking at its outcomes.
- I can connect likelihood language to a probability value between 0 and 1.
What success looks like
- I can sort four or more events into the correct likelihood category.
- I can justify where I placed an event on the likelihood scale using evidence from the outcomes.
- I can use certain, likely, unlikely, impossible, and equally likely correctly in a sentence about a real event.
- I can match each likelihood word to an approximate spot on a 0-to-1 number line.
Describe how likely an event is to happen using precise probability language.
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.
Certain
An event that will always happen. Its probability is 1, or 100%.
Impossible
An event that can never happen. Its probability is 0, or 0%.
Likely
An event that has a good chance of happening — more likely than not, though not guaranteed.
Unlikely
An event that has a small chance of happening — less likely than not, though still possible.
Equally Likely
Two or more outcomes that have the exact same chance of happening.
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.
Using Data to Weigh Risk
Soon you'll meet actuaries, the professionals who spend their careers deciding exactly how likely risky events are, like a car accident or a bad storm. Every one of those decisions starts with the same likelihood language you're learning today, just with much bigger numbers behind it.
Where Does It Fall?
Every event you can imagine has a spot on a single scale, and today you'll learn to name that spot precisely.
Picture a number line that runs from 0 to 1, with every possible event living somewhere on it. On the far left sits anything that is impossibleAn event that can never happen. Its probability is 0, or 0%. — rolling a 7 on a standard number cube, for example. On the far right sits anything that is certainAn event that will always happen. Its probability is 1, or 100%. — the sun rising tomorrow, or picking a red marble from a bag that only has red marbles in it. Almost everything else falls somewhere in between, and that's where the more interesting words come in.
An event is likelyAn event that has a good chance of happening — more likely than not, though not guaranteed. when it has a good chance of happening, even though it isn't guaranteed, like drawing a blue marble from a bag that is mostly blue. An event is unlikelyAn event that has a small chance of happening — less likely than not, though still possible. when the odds are stacked against it but it could still occur, like drawing the one yellow marble out of a bag of twenty. And when two outcomes have the exact same chance, like flipping heads or tails on a fair coin, mathematicians call them equally likelyTwo or more outcomes that have the exact same chance of happening.. Naming where an event falls is the first step toward calculating exactly how likely it is, which is exactly what you'll do in the next few lessons.
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 equal sections
- C. A small bag of colored counters or marbles
- D. Your Data Journal
- E. A calculator (optional)
Before naming a likelihood, always count the total outcomes and the favorable outcomes first — the words come after the count, never before it.
Likelihood Lab
Today's lab gives you real outcome counts so your likelihood words are backed by evidence, not a guess.
Build a Likelihood Line
You'll build a physical number line and place real events on it using evidence from their outcomes.
Data Journal Entry
Accountability Checklist
Which Word Fits?
A spinner has 8 equal sections: 1 is red and 7 are blue. Is landing on red likely or unlikely? Use the outcome counts to justify your answer.
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