$36.$ Professor Hartwig has a personal auto policy $($PAP$)$ with $$250/$$$500/$$$50$ in limits$.$ Suppose that I am involved in an accident with another vehicle and am found to be at fault. If that driver, the sole occupant of that vehicle, sues me and I am found liable for $$500,000$ in medical damages to that driver, how much will my insurance pay?

a$.$ $$0$

b$.$ $$50,000$

c$.$ $$100,000$

d$.$ $$250,000$

e$.$ $$300,000$

f$.$ $$500,000$