This is a problem from an old Society of Actuaries Exam P (probability) exam:
A family buys two policies from the same insurance company. Losses under the two policies are independent and have continuous uniform distributions on the interval from 0 to 10. One policy has a deductible of 1 and the other has a deductible of 2. The family experiences exactly one loss under each policy.
Calculate the probability that the total benefit paid to the family does not exceed 5.
I don't understand this language: the second sentence says
$$X:=\text{Loss}_{\text{Policy 1}}\sim\text{Unif}[0,10]$$ $$Y:=\text{Loss}_{\text{Policy 2}}\sim\text{Unif}[0,10]$$
where $X$ and $Y$ are independent. So the losses are uniformly distributed. But nothing is said explicitly about the benefit each policy will pay.
Am I supposed to assume that each policy will pay the entire loss after the deductible? Otherwise there simply is not enough information to answer the question.
But it seems absurd to me for the Society of Actuaries to require candidates to make an assumption that is implausible in practice: insurance policies often don't pay the entire loss after a deductible. There is usually some upper bound you know in advance.