Practice Calculating Probability | The Center for Quantitative Studies | Studio Aletheia
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Practice Calculating Probability

Lesson 19 · Guided Practice, Find the Probability of Simple Events

Yesterday you learned to calculate a probability from outcome counts. Today you'll get faster and more flexible, working with larger totals and starting from a probability to figure out matching outcomes.

Focus Probability Fluency
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's mini-lesson recaps yesterday's calculation and stretches it in two new directions.

Targets

What I will learn

  • I can calculate the probability of a simple event from a data set with up to 200 outcomes.
  • I can move flexibly between fraction, decimal, and percent forms of a probability.
  • I can work backward from a probability to figure out possible outcome counts.
  • I can compare the probabilities of two different simple events.
Success Criteria

What success looks like

  • I can calculate at least four probabilities correctly as simplified fractions.
  • I can convert any probability fraction to a decimal and percent for common denominators.
  • I can find a possible set of outcomes that matches a given probability.
  • I can state which of two events has the greater probability and explain why.
Standard 6.DPSR.2.2

Build fluency calculating and comparing the probability of simple events.

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 · Connect

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

Practice Makes the Numbers Trustworthy

Actuaries run the same probability calculation thousands of times a year until it becomes second nature, because a single mistake can mean a company charges the wrong price for real people. The fluency you're building today with fractions, decimals, and percents is exactly what makes that trust possible.

Mini-Lesson

Getting Faster and More Flexible

Today's mini-lesson recaps yesterday's calculation and stretches it in two new directions.

Yesterday you found the 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. of 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. by counting favorable outcomes over total outcomes. Today the total outcomes get bigger, up to 200, which means your fraction skills matter more than ever. A bag of 200 marbles with 50 red ones gives a probability of 50/200, which simplifies all the way down to 1/4, exactly the same probability as a bag of just 4 marbles with 1 red one. The size of the group changes, but the probability, and the story it tells, stays the same.

Today you'll also practice working backward. If you're told an event has a probability of 1/5, you can build a scenario that matches: a spinner with 5 equal sections and 1 favorable one, or a bag of 20 marbles with 4 favorable ones, since 4/20 also simplifies to 1/5. Being able to move in both directions, from outcomes to probability and from probability to outcomes, is what lets you compare two events fairly, even when they come from very different-sized data sets.

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
Event A: probability 3/10. Event B: probability 25%. Which event is more likely? Show your reasoning by converting both to the same form.
Toolkit

Materials for the Data Lab.

  • A. A spinner divided into 10 equal sections
  • B. A bag of 20 or 50 marbles
  • C. Fraction/decimal/percent conversion chart
  • D. Your Data Journal
  • E. A calculator (optional)
Non-negotiable routine

Before comparing two probabilities, convert both to the same form — fraction, decimal, or percent — so the comparison is fair.

Guided Practice

Probability Lab: Round Two

Today's lab mixes forward calculations with backward ones, so you build true flexibility.

Data Lab
Some scenarios below give you outcomes to calculate a probability from; others give you a probability and ask you to build matching outcomes.
1 · Identify
Identify which scenarios give you outcomes and which give you a probability to match.
2 · Calculate
Calculate the probability for the outcome-based scenarios as a fraction, decimal, and percent.
3 · Connect
Connect each given probability to a matching set of outcomes you design.
4 · Compare
Compare two probabilities from today's lab and state which event is more likely.
Hands-On

Match the Probability

You'll design your own spinner or bag to match a target probability, then check it against a partner's.

1
Choose: Choose one target probability from today's lab (1/5 or 40%).
2
Design: Design a spinner or bag of marbles with outcome counts that match your target probability.
3
Verify: Verify your design by calculating its probability and simplifying to check it matches.
4
Trade: Trade designs with a partner and verify each other's probability calculation.
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

Build the Match

Design a bag of 25 marbles where the probability of pulling a green marble is exactly 20%. State how many green marbles and how many total marbles are in your bag.

Lesson 19 · Guided Practice, Find the Probability of Simple Events

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