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← Secondary · Ages 14–18

Project-based Lesson

What Does Road Risk Cost?

Conditional probability in a realistic business case

Is it fair for the price of car insurance to depend only on age – or does behaviour on the road tell us more? Students act as the board of directors of the fictional insurer “Alpha Safe”, analyse a teaching database of 1,000 drivers and turn their intuition into an insurance card they can defend.

  • Ages 16–18
  • Maths · Probability
  • About 80 minutes (2 periods)
  • Teamwork
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Project-based Lesson Ages 16–18

Maths • Probability • Business

  • P(A|B)
  • Data
  • Insurance case

About the data

All the numbers, client names and the company “Alpha Safe” are fictional data created for teaching. They are not official road-safety or police statistics and do not come from a real insurance company. The differences between the age groups are also invented for teaching purposes.

How the lesson works

Six steps take students from a first intuition to a finished insurance card.

  1. Intuition first

    Teams take a position on three clients from different age groups – without calculating anything.

  2. A teaching database

    They explore a fictional database of 1,000 drivers by age group, traffic violations and road crashes.

  3. Violations and crashes

    They identify the conditioning group, build the fraction themselves and compare P(crash | violation) with P(violation | crash).

  4. Age and profile

    They calculate the risk under two conditions for each client and solve a transfer task with new numbers.

  5. The insurance card

    They set a risk category and a price for each client and justify their decisions to the “board”.

  6. Exit card

    They sum up what they have learned and where else conditional probability is used.

Maths and skills

Maths covered

  • Conditional probability P(A|B) from a two-way table
  • Identifying the conditioning group and the denominator
  • Reversing a condition: P(A|B) and P(B|A)
  • Comparing risks with a ratio
  • Conditions with two characteristics at once

Reasoning and decision-making

  • Telling statistical association apart from causation
  • Comparing proportions instead of raw counts
  • Setting prices and justifying them with data
  • Working together and presenting a decision

Teacher guidance

Short practical guidance is also available in the lesson, under the For teachers button.

What you need

  • One device per team
  • No printed materials
  • About 80 minutes (two periods)

Running the lesson

  • Numerical answers are checked automatically, with a hint after common mistakes.
  • There is no single correct price – the business argument is for you to discuss and assess.
  • Open questions are clearly marked as not graded.
  • Progress is saved automatically on the device.

Ready to price the risk?

Open the interactive lesson on your students' devices.

Start the interactive lesson