Intervention Playbook Teacher Guide Intervention Playbook
Lesson: Expected Value Decisions
Teacher Resource
Learning Objective
Students will weigh possible outcomes of a decision by assigning probabilities to payoff values and finding expected values to make informed comparisons (Colorado HS.S-MD.A.5).
Targeted Skills
Constructing Payoff Tables
Probability Weighting
Expected Value Comparison
Small Group Delivery Script
1
The "Why" Hook (3 mins)
"Imagine you're an insurance agent or a business owner. You can't see the future, but you can see the math. How do we know if a risk is actually worth it?"
2
Guided Modeling: The Payoff Table (7 mins)
Use the Decision Desk Slides . Emphasize that EV isn't what *will* happen once, but what happens *on average* over many repeats.
Key Verbal Prompt: "Multiply the value by its chance. Do that for every row. Then add them all up. The sum is your expected value."
3
Scaffolded Practice (15 mins)
Hand out the Outcome Odds Worksheet . Circulate and check for the "Probability Trap" (students often try to average the probabilities instead of the products).
Progress Monitoring Tool
Record student performance on the Risk Report Assessment exit ticket.
Student Name Correct Table? Calculated EV? Correct Decision? Notes / Next Steps ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐
Common Pitfalls & Misconceptions
The "Single Trial" Bias
Students think the EV is the amount they will actually win. Explain: "You can't actually win $14.50 in a game where you only win $10 or $20. EV is the long-term average."
Summing to 1
Remind students to always check if their probabilities sum to 1.0 (100%). If they don't, the payoff table is missing an outcome!
Decision Desk Slides Decision
Desk
Using Expected Value to Win Big
The Definition
The Expected Value (EV) is the weighted average of all possible outcomes.
"It's what you would expect to happen, on average, if you made the same decision many, many times."
\[ E(X) = \sum x \cdot P(x) \]
The Payoff Table
To calculate EV, we organize our data into columns:
1 Identify all Outcomes
2 Assign Payoff Values (\(x\))
3 Find Probabilities (\(P(x)\))
Outcome Value (\(x\)) Prob (\(P(x)\)) Win Big +$100 0.20 Win Small +$20 0.50 Lose -$50 0.30
Scenario:
The Food Truck
A taco truck owner is deciding whether to buy a permit for a massive downtown festival.
The Odds
60% chance of Sunny: Profit $3,00040% chance of Rain: Loss -$1,000
Calculation Check:
\( (3000 \cdot 0.60) + (-1000 \cdot 0.40) \)
\( 1800 - 400 = \mathbf{\$1,400} \)
The expected profit is $1,400. Worth the risk?
Compare the EV
Choice A: Steady Path
Guaranteed outcome:
+$500
"Zero risk, fixed payoff."
Choice B: High Stakes
25% chance: +$3,000
75% chance: $0
Expected Value:
+$750
Choice B has a higher Expected Value, even though it's riskier!
Outcome Odds Worksheet Outcome Odds
Expected Value Decision Matrix
Name:
Date:
The EV Formula
Multiply across, then add down.
Expected Value = \(\sum (\text{Value} \times \text{Probability})\)
1
Scenario: The New Product Launch
A tech company is deciding whether to launch a new smartwatch. There are three possible outcomes for sales: High, Average, and Low. Use the data below to find the Expected Value of the launch.
Outcome Profit Value (\(x\)) Probability (\(P(x)\)) Calculation (\(x \cdot P(x)\)) High Success +$500,000 0.25 Average Success +$100,000 0.50
|
| Failure/Loss | -$200,000 | 0.25 |
|
Total Expected Value:
$
2
The Big Decision: Insurance vs. Savings
A shipping company must decide between buying insurance for $5,000 or self-insuring (saving the money). If a storm hits (10% chance), they lose $40,000 worth of cargo.
Plan A: Buy Insurance
You pay $5,000 no matter what.
EV for Plan A:
-$5,000
Plan B: Self-Insure
Storm (0.10): -$40,000
Clear (0.90): $0
Calculate EV for Plan B:
Final Recommendation:
Which plan has the higher (less negative) expected value? Why?
Risk Report Assessment Progress Monitor
Risk Report
Exit Ticket Assessment
Agent Name
Shift/Date
The Brief: A sports promoter is planning an outdoor game. If it stays dry (70% chance), they earn $10,000 . If it rains (30% chance), they lose $4,000 in cleanup costs.
1 Complete the Payoff Table
Outcome Value (\(x\)) Prob (\(P(x)\)) Dry Weather $10,000 Rainy Weather -$4,000
2 Calculate the Expected Value
EV Result: $
3 Decision Time
Should the promoter go ahead with the game based on the math? Explain.
Risk Management Division • Statistical Audit
