Risk Assessment Through Probability

Overview

In this lesson, students connect probability thinking to risk assessment by evaluating different choices using expected value. This builds from Lesson 1’s focus on sample spaces and probability basics, and prepares for later lessons on comparing strategies in more complex scenarios.

Learning intentions

Students will be able to:

• Define events using sample-space language (subsets, “and,” “or,” “not”).
• Calculate expected value for a random variable based on a probability distribution.
• Compare two risk-management choices by evaluating expected value using reasonable probabilities.
• Explain conditional probability in everyday risk situations.

Success criteria

Students can:

• Represent an insurance/finance scenario as events in a sample space.
• Compute expected value from a probability distribution and interpret it as an average outcome.
• Justify which option is “better” using expected value rather than intuition alone.
• Use conditional probability terms correctly when describing risk comparisons.

Curriculum links

• Statistics and Probability—Using Probability to Make Decisions: evaluate and compare strategies using expected values.
• Statistics and Probability—Conditional Probability and the Rules of Probability: describe events using unions/intersections/complements and recognize conditional probability.
• Statistics and Probability—Using Probability to Make Decisions: define random variables and calculate expected value from a probability distribution.

Lesson structure (30 minutes)

1. 0–4 min · Quick launch (scenario + prediction). Teacher displays two short policy options (high deductible vs. low deductible) with the same coverage limit but different costs, and asks students which seems safer; students make a quick prediction and give a reason in one sentence.
2. 4–10 min · Event language mini-teach. Teacher models a sample space for outcomes like “minor accident” or “major accident” or “no accident,” then shows how to describe events as subsets and combine them (“minor or major,” “not minor”); students complete a 3-item event-description prompt using words like “event,” “subset,” “and/or/not.”
3. 10–18 min · Expected value modeling (guided). Teacher introduces a random variable X for “net cost” under one policy, lists possible values (e.g., deductible + repair costs) and their theoretical probabilities, then calculates expected value step-by-step; students compute expected value for a second policy using the provided probabilities.
4. 18–24 min · Compare strategies with justification. Teacher prompts students to compare the two expected values and choose which policy has lower expected net cost (or higher expected value, depending on setup); students write a brief comparison claim using the phrase “Based on expected value…”.
5. 24–28 min · Conditional probability check (risk framing). Teacher gives a common risk statement (e.g., “chance of a claim given an accident” vs. “chance of an accident given a claim”) and has students identify which probability is conditional and what it means in context; students answer on mini-slips.
6. 28–30 min · Exit ticket (single task). Students complete one problem: compute one additional expected value term and state which option is better using that result.

Resources

• Printed scenario cards for two policy options (high deductible vs low deductible)
• Handout with a sample space and event-description items (“minor,” “major,” “no accident”)
• Expected value table template (outcomes, probabilities, X values, probability×X)
• Scientific calculators (optional) or class calculators
• Student mini-slips for conditional probability identification
• Exit ticket sheet
• Projector/board markers

Assessment

• Formative check during event-language mini-teach: collect/spot-check student responses to ensure correct use of “and/or/not.”
• Formative check during expected value modeling: monitor student calculations in the table, looking for errors in probability×X and summing.
• Exit ticket: one short expected value computation plus an option choice justified by expected value.

Differentiation

• Support: Provide sentence starters for event descriptions (“The event ___ is the set of outcomes where…”; “___ or ___ includes outcomes…”; “The complement of ___ includes…”).
• Support: Provide a partially filled expected value table for students who need the structure; gradually release responsibility.
• Extension: For students ready to go further, ask them to discuss how changing probabilities (within “reasonable” bounds) could flip the recommendation.
• EAL/SEN: Allow students to discuss first with a partner using everyday language, then convert to math vocabulary (event, random variable, expected value, conditional probability).