Suppose a family has 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?

Answer: 8

Please show your work + provide explanation.