Likely and Unlikely Events

Active learning helps students grasp likely and unlikely events because probability concepts are abstract and need concrete, repeated experiences to build intuition. Sorting, spinning, and voting make chance visible, turning words like ‘likely’ into lived understanding rather than memorized definitions.

• Foundation
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Identify all possible outcomes for simple chance experiments.
2. Classify events as certain, likely, unlikely, or impossible.
3. Compare the likelihood of two different outcomes in a chance experiment.
4. Explain why one event is more likely than another based on the sample space.

⏱ 30 min·Pairs

Pairs: Counter Bag Trials

Fill bags with varying numbers of red and blue counters, such as 3 red and 1 blue. Pairs predict the more likely color, draw with replacement 20 times, tally on charts, and discuss matches to predictions. Share one insight with the class.

Prepare & details

If I pick a counter from this bag without looking, is it more likely to be red or blue?

Facilitation Tip: During Counter Bag Trials, circulate and ask pairs to predict the next draw before they pick, making likelihood a conversation rather than a guess.

⏱ 40 min·Small Groups

Small Groups: Unequal Spinner Stations

Prepare three spinners with unequal sections (e.g., 75% one color, 25% another). Groups spin each 15 times, record outcomes on group sheets, rotate stations, and compare data patterns across spinners.

Prepare & details

What events are very likely to happen today?

Facilitation Tip: At Unequal Spinner Stations, have students first predict the most likely section without spinning, then test their ideas to see if their reasoning matches the results.

⏱ 25 min·Whole Class

Whole Class: School Events Vote

Show images of events like 'it rains at recess' or 'teacher arrives late'. Class votes likely or unlikely using hand signals, tallies on board, and justifies choices. Revisit after observing real events.

Prepare & details

Can you think of something that is unlikely to happen at school?

Facilitation Tip: In the School Events Vote, model how to phrase certain, likely, unlikely, and impossible using school routines before students share their own examples.

⏱ 20 min·Individual

Individual: Outcome Listing Game

Provide simple scenarios like 'pick a shape from three: circle, square, triangle'. Students list or draw all possible outcomes, then simulate draws with cards and check completeness against class model.

Prepare & details

If I pick a counter from this bag without looking, is it more likely to be red or blue?

Teaching This Topic

Teach this by balancing prediction, trial, and reflection in every activity. Avoid rushing to labels before students have experienced chance outcomes multiple times. Research shows that repeated trials with visual recording help students move from ‘all outcomes are equal’ to proportional reasoning. Keep language consistent and tie it directly to what they see and do.

What to Expect

Successful learning shows when students use probability language correctly, justify choices with evidence, and connect counts to likelihood without relying on guessing. They should explain why one outcome is more likely than another using the materials in front of them.

Watch Out for These Misconceptions

Common Misconception

During Counter Bag Trials, watch for students who assume the first few draws represent the whole bag’s proportions.

What to Teach Instead

Pause after 10 draws and ask pairs to compare their tallies to the actual contents. Have them adjust predictions for the next 10 draws based on what they now know.

Common Misconception

During Unequal Spinner Stations, watch for students who think a section that ‘looks bigger’ is always more likely, regardless of proportions.

What to Teach Instead

Ask students to measure spinner sections with paper clips or mark 10 equal parts, then tally outcomes to see if the visual matches the math.

Common Misconception

During Outcome Listing Game, watch for students who list only outcomes they saw in early trials and miss possible but unobserved ones.

What to Teach Instead

Before any trials, have students list every possible outcome on a whiteboard and check it against actual results, circling any they missed in their initial writing.

Assessment Ideas

Quick Check

After Counter Bag Trials, present a new bag with 3 red and 7 blue counters. Ask students to circle the color they are more likely to pick and write one sentence explaining why using the bag contents.

Exit Ticket

During Unequal Spinner Stations, hand each student a spinner card with unequal sections. Ask them to label one section ‘Most likely’, one ‘Least likely’, and one ‘Possible but not most likely’, then explain their choices to a partner.

Discussion Prompt

During School Events Vote, ask each student to share one event they consider certain, one impossible, and one likely for the school day. Listen for correct use of probability language tied to school routines and examples.

Extensions & Scaffolding

• Challenge students to design their own unequal spinner with three colors and write a sentence explaining which color is most likely and why.
• Scaffolding: Provide spinners pre-labeled with numbers 1–4 and counters in 3:1 ratios so students focus on comparing likelihood without making their own sets first.
• Deeper exploration: Ask students to create a bar graph after Counter Bag Trials showing how many times each color was picked and predict what would happen if they did 50 more draws.

Key Vocabulary

Sample Space	The set of all possible outcomes of a chance experiment. For example, the sample space for flipping a coin is heads and tails.
Outcome	A single possible result of a chance experiment. For example, getting a '3' when rolling a die is one outcome.
Likely	An event that has a good chance of happening. For example, it is likely to rain if the sky is full of dark clouds.
Unlikely	An event that has a small chance of happening. For example, it is unlikely to snow in Australia during summer.
Certain	An event that is guaranteed to happen. For example, the sun is certain to rise tomorrow.
Impossible	An event that cannot happen. For example, it is impossible for a cat to fly without assistance.