P: Bayes’ rule starts with the base rate
A conditional claim probability does not tell you the probability that a claimant belongs to a risk group. Build joint probabilities first, then condition on the event actually observed. This also makes the denominator visible instead of treating Bayes’ rule as a formula to memorise.
Worked example or practice scenario
In an original population, 10% are high risk. Claim probabilities are 20% for high risk and 5% for other risks. Per 1,000 people, expected claims are 20 and 45. Thus P(high risk | claim) = 20/65 = 30.77%, not 80%.
Try this next
Change the high-risk share to 2%, leaving claim probabilities fixed. Expected claimant counts become 4 and 49 per 1,000, so the posterior is 4/53. Explain why the result falls before calculating it.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.