Suppose a family have saved enough for a 10 day vacation (the only one they will be able to take for 10 years) and has a utility function U=V^1/2 (where V is the number of healthy vacation days they experience). Suppose they are not a particularly healthy family and the probability that someone will have a vacation-ruining illness (V=0) is 20%. What is the expected value of V?

Continuing with the same family from the preceding question, what is the greatest (integer) number of vacation days the family would be willing to give up in order to guarantee a healthy vacation?

Continuing with the same family from the preceding question, suppose a risk neutral insurance company exists to provide vacation insurance. Suppose further that each vacation day requires a constant expenditure, and this expenditure is standard across everybody. This allows us to simplify the problem by considering all payments to be in terms of vacation days. What is the least the insurance company would charge (in terms of vacation days)?