An insurance company offers doctors malpractice insurance. Assume that malpractice claims against careful doctors cost $$\$ 5,000$$ on average over the term of the policy and settling malpractice claims against reckless doctors costs $$\$ 30,000$$. Doctors know whether they are reckless or careful, but the insurance company only knows that $10 \%$ of doctors are reckless. How much do insurance companies have to charge for malpractice insurance to break even?
a. $$\$ 5,000$$
b. $$\$ 7,500$$
c. $$\$ 27,500$$
d. $$\$ 30,000$$