help with question 3

3. [5 points each] An agent faces a health risk: she is either healthy and making $ 100 with probability 0.8 or sick and making $0 with probability 0.2. The agent can buy health insurance that gives benefit of $68 only if she is sick, at premium of $19. For each of the following utility functions, find whether the agent buys the health insurance. Provide intuition. (a) u (c) = co.5 (b) u (c) = c (c) u (c) = c2