Final answer:
The umbrella policy would pay $10,000 after a $12,000 personal injury liability claim, as the self-insured retention (SIR) of $2,000 must be paid by the insured first.
Step-by-step explanation:
If an insured has a personal umbrella with a $2,000 self-insured retention (SIR), and there is no other policy involved, we need to calculate the amount the umbrella policy would pay after a $12,000 personal injury liability claim. The self-insured retention is the amount the insured must pay out-of-pocket before the umbrella policy covers the remaining costs. In this case, the insured would pay the first $2,000 of the claim, and the umbrella policy would pay the remaining $10,000.
So the answer to the question, "How much would the umbrella pay after a $12,000 personal injury liability claim?" is C) $10,000.