Final answer:
Sophie's insurance pays $100,000 as the primary coverage, and John's policy pays the remaining $200,000 as secondary coverage for the $300,000 bodily injury liability.
Step-by-step explanation:
When two auto insurance policies are involved in a claim, the primary policy typically pays out first, up to its policy limits, before the secondary policy comes into play. In this case, because John was driving Sophie's car, Sophie's insurance would be considered the primary policy and John's as secondary or excess coverage.
Sophie's policy has limits of $100,000 per person for bodily injury, which means her policy would pay $100,000 towards the total liability of $300,000. After Sophie's policy limit has been exhausted, John's policy would then cover the remaining $200,000, as his policy has higher limits of $250,000 per person for bodily injury.
In summary, Sophie's policy would pay out the policy limit of $100,000, and John's policy would pay the remaining $200,000 of the bodily injury liability.