Studio Aletheia · The Center for Quantitative Studies
6.DPSR.2.1SC 6th Grade Math
Likelihood on the Job
Lesson 17 · Application, State the Likelihood of an Event
Actuaries make a living turning likelihood language into real decisions about risk and price. Today you'll step into that role, using outcome data to judge how likely different insurance-style events are and explain what that means for a real decision.
Learning Targets and Success Criteria
Today you'll see exactly how the likelihood words you've been using turn into real financial decisions.
What I will learn
- I can use likelihood language to describe risk scenarios in a real-world context.
- I can explain how likelihood affects a decision like setting a price or a policy.
- I can compare risk scenarios and identify which is more likely to lead to a claim.
- I can justify a recommendation using likelihood evidence.
What success looks like
- I can describe at least three risk scenarios using correct likelihood words.
- I can explain in writing why a more likely risk should cost more to insure.
- I can compare two risk scenarios and state which is riskier, with evidence.
- I can write a one-sentence recommendation backed by outcome counts.
Apply likelihood language to real risk scenarios the way an actuary would.
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.
Certain
An event that will always happen. Its probability is 1, or 100%.
Impossible
An event that can never happen. Its probability is 0, or 0%.
Likely
An event that has a good chance of happening — more likely than not, though not guaranteed.
Unlikely
An event that has a small chance of happening — less likely than not, though still possible.
Equally Likely
Two or more outcomes that have the exact same chance of happening.
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.
Pricing Auto Insurance
An auto insurance actuary looks at thousands of drivers and counts how many with a certain profile file a claim in a year. If claims are likely for a group, like drivers under 20, the actuary sets a higher price; if claims are unlikely, the price drops. Every price on a family's insurance bill started as a likelihood judgment just like the ones you'll make today.
Setting Home Insurance Rates
A home insurance actuary studies weather data for a region and judges how likely severe storms are each year. A region where damaging storms are likely gets higher premiums, one where they're unlikely gets lower ones, and regions where storms are almost impossible pay very little for that coverage at all.
Likelihood Sets the Price
Today you'll see exactly how the likelihood words you've been using turn into real financial decisions.
Every insurance price starts with a likelihood judgment. An actuary looks at a group of people or homes and asks the same question you've been asking: is this event likelyAn event that has a good chance of happening — more likely than not, though not guaranteed. or unlikelyAn event that has a small chance of happening — less likely than not, though still possible.? If a type of accident is likely for a group, the actuary charges that group more, because the company is more likely to have to pay out a claim. If it's unlikely, the price comes down.
The extreme ends of the scale matter too. Coverage for something impossibleAn event that can never happen. Its probability is 0, or 0%., like insuring a house against being hit by a dinosaur, would never be sold, because no company would insure a risk with zero chance of happening. And when two groups are equally likelyTwo or more outcomes that have the exact same chance of happening. to file a claim, actuaries charge them the same price, because fairness in pricing means matching the price to the actual risk, not a guess. The one word that shows up in every policy's fine print is certainAn event that will always happen. Its probability is 1, or 100%. — because the only thing an insurance company can be certain of is that it must be ready to pay when a likely event happens.
Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.
Materials for the Data Lab.
- A. Risk scenario cards
- B. A spinner divided into equal sections
- C. A bag of colored counters (to model claim rates)
- D. Your Data Journal
- E. A calculator (optional)
Before recommending a price or policy, state the likelihood word for the risk and name the evidence behind it.
Risk Lab
Today's lab has you act as a junior actuary, judging real-style risk scenarios and recommending a price direction.
Set the Price
You'll act as a junior actuary team, ranking today's risk scenarios and recommending prices.
Data Journal Entry
Accountability Checklist
Who Pays More?
A pool company insures 5 backyard pools. In 4 of the last 5 years, at least one pool needed a costly repair. Is a repair claim likely or unlikely in a given year? Use that word to recommend whether this group should pay a higher or lower insurance price.
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