A risk averse person with a von-Neumann-Morgenstern utility

A risk averse person with a von-Neumann-Morgenstern utility index of: U = 1n(Y)
has a 20% chance that a disaster will reduce her regular income of $100,000 to zero.
She can buy insurance at a rate of $0.40 per dollar of coverage.
a) Will she fully, under, or over-insure against this risk, and why?
b) What is her optimal bundle of contingent claims?
c) How much insurance will she buy and at what cost?