Studio Aletheia · The Center for Quantitative Studies
6.DPSR.2.2SC 6th Grade Math
Pricing Risk with Probability
Lesson 20 · Application, Find the Probability of Simple Events
An actuary's entire job rests on one calculation you now know how to do: turning outcome counts into a probability. Today you'll use real probability values to make the same pricing decisions actuaries make every day.
Learning Targets and Success Criteria
Today you'll see how a calculated probability turns directly into a pricing decision.
What I will learn
- I can calculate the probability of a claim-style event from a small data set.
- I can convert a probability into a decimal or percent to compare pricing risk.
- I can rank groups by their probability of a costly event.
- I can justify a pricing recommendation using a calculated probability.
What success looks like
- I can calculate at least three claim-style probabilities correctly.
- I can convert each probability into a decimal and a percent for comparison.
- I can rank at least three groups from lowest to highest probability of a claim.
- I can write a one- to two-sentence pricing recommendation backed by a probability value.
Use calculated probability to make and justify a real pricing decision.
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.
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.
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.
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.
Calculating a Claim Rate
An auto actuary looks at 100 drivers in a group and counts how many filed a claim last year. If 8 of them did, the probability of a claim is 8/100, or 8%. That single percent becomes the starting point for how much every driver in that group pays.
Comparing Risk Pools
Insurance companies group people into risk pools and calculate a probability of a claim for each pool. A pool with a higher probability of a claim, say 15% instead of 5%, gets a higher price, because the company expects to pay out more often for that group. Comparing probabilities fairly, in the same form, is what keeps pricing honest.
From Percent to Price
Today you'll see how a calculated probability turns directly into a pricing decision.
Every insurance price is built on a 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. calculation. An actuary studies a group of policyholders and identifies one simple eventAn event made up of a single outcome, or a small set of favorable outcomes, from all the possible outcomes in a situation. they care about, like filing a claim in a given year. If 10 out of 200 drivers in a group filed a claim, the probability is 10/200, which simplifies to 1/20, or 5%.
That percent doesn't stay abstract for long. A company that expects a claim 5% of the time has to collect enough money from the whole group to cover those claims and still run the business, so the price gets set using that exact number. Compare two groups: one with a 5% probability of a claim and another with a 20% probability, and the second group will always pay more, because the math says a claim is four times more likely there. Calculating probability accurately isn't just a math exercise, it's the difference between a fair price and an unfair one.
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 with outcome counts
- B. Fraction/decimal/percent conversion chart
- C. A calculator
- D. Your Data Journal
- E. A ranking chart or sticky notes
Before recommending a price, calculate the probability, convert it to a percent, and compare it directly to the other group's percent.
Pricing Lab
Today you'll act as a junior actuary team calculating probabilities to recommend pricing across several groups.
Set the Rates
You'll calculate claim probabilities for all four groups and build a simple rate recommendation chart.
Data Journal Entry
Accountability Checklist
Whose Price Goes Up?
Group A: 6 claims out of 200 policyholders. Group B: 6 claims out of 50 policyholders. Calculate the probability of a claim for each group and recommend which group should pay more.
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