Probability: Putting It All Together | The Center for Quantitative Studies | Studio Aletheia
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Probability: Putting It All Together

Lesson 24 · Consolidation, 6.DPSR.2 Wrap-Up

Over the last nine lessons you've described likelihood, calculated probability, and found complements. Today you'll pull all three skills together and show that you can move between them without missing a step.

Focus Probability Standard Review
Accountability Data Journal + Exit Ticket
Indicator Describe likelihood, calculate probability, and find complements across...
The Center for Quantitative Studies Color Palette Aletheian Green · Aletheian Gold
Learning Targets

Learning Targets and Success Criteria

Today's mini-lesson connects everything you've learned about probability into one toolkit.

Targets

What I will learn

  • I can describe the likelihood of an event using certain, likely, unlikely, impossible, or equally likely.
  • I can calculate the probability of a simple event as a fraction, decimal, or percent.
  • I can calculate the complement of an event using P(not A) = 1 − P(A).
  • I can choose the right probability tool for a new problem without being told which one to use.
Success Criteria

What success looks like

  • I can correctly describe the likelihood of at least three new events.
  • I can correctly calculate at least three new simple-event probabilities.
  • I can correctly calculate at least three complements and verify each with addition.
  • I can solve a mixed review problem that requires more than one of these skills.
Standard 6.DPSR.2

Review and connect likelihood, probability, and complement across the whole standard.

6.DPSR.2 — Calculate and interpret probability: describe the likelihood of an event, find the probability of a simple event, and calculate the probability of its complement.
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 · Describe

Certain

An event that will always happen. Its probability is 1, or 100%.

02 · Describe

Impossible

An event that can never happen. Its probability is 0, or 0%.

03 · Judge

Likely

An event that has a good chance of happening — more likely than not, though not guaranteed.

04 · Judge

Unlikely

An event that has a small chance of happening — less likely than not, though still possible.

05 · Compare

Equally Likely

Two or more outcomes that have the exact same chance of happening.

06 · 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.

07 · 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.

08 · Calculate

Complementary Event

The event that everything that is NOT the original event happens instead; P(not A) = 1 − P(A).

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

One Job, Three Tools

Every calculation an actuary runs uses some combination of the three skills you've just reviewed: judging likelihood, calculating a probability, and finding a complement. Reflect on which of the three felt most natural to you today, because that instinct is exactly the kind of thinking actuaries rely on.

Mini-Lesson

Three Skills, One Standard

Today's mini-lesson connects everything you've learned about probability into one toolkit.

This standard began with language. You learned to call an event certainAn event that will always happen. Its probability is 1, or 100%., impossibleAn event that can never happen. Its probability is 0, or 0%., likelyAn event that has a good chance of happening — more likely than not, though not guaranteed., unlikelyAn event that has a small chance of happening — less likely than not, though still possible., or equally likelyTwo or more outcomes that have the exact same chance of happening. just by comparing outcome counts. That language turned out to be a preview of an exact number.

From there, you learned to calculate a 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. for any simple eventAn event made up of a single outcome, or a small set of favorable outcomes, from all the possible outcomes in a situation., as a fraction, decimal, or percent, and finally you learned the complement rule, which finds the probability of a complementary eventThe event that everything that is NOT the original event happens instead; P(not A) = 1 − P(A). with a single subtraction. All three skills describe the same underlying idea: how much of the total space of outcomes belongs to the event you care about. Today's job is to move between the three without hesitating over which one to use.

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, 15 blue. Describe the likelihood of pulling red in words, calculate its probability, and find the probability of its complement.
Toolkit

Materials for the Data Lab.

  • A. A bag of 20 or 25 marbles
  • B. A spinner divided into equal sections
  • C. Fraction/decimal/percent conversion chart
  • D. Your Data Journal
  • E. A calculator (optional)
Non-negotiable routine

For any new probability problem, first describe the likelihood in words, then calculate the number, then check the complement.

Guided Practice

Probability Review Lab

Today's lab mixes all three skills from the standard into one set of scenarios.

Data Lab
Each scenario below can be described, calculated, and complemented — work through all three for each one.
1 · Review
Review each scenario and describe its likelihood using one of the five likelihood words.
2 · Compare
Compare two scenarios and state which has the greater probability.
3 · Solve
Solve for the probability and the complement of each scenario.
4 · Reflect
Reflect on which of the three skills (likelihood, probability, complement) felt hardest this unit, and why.
Hands-On

Full Probability Challenge

You'll work all four scenarios through all three skills from the standard, start to finish.

1
Describe: Describe the likelihood of each scenario's event in words.
2
Calculate: Calculate the probability of each event as a fraction, decimal, and percent.
3
Complement: Calculate the complement of each event and verify it adds to 1 with the original probability.
4
Reflect: Reflect in writing on one strategy that helped you the most across this standard.
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

Show What You Know

A spinner has 4 equal sections, 1 of which is purple. Describe the likelihood of landing on purple, calculate its probability, and find the probability of its complementary event.

Lesson 24 · Consolidation, 6.DPSR.2 Wrap-Up

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