The probability that a random person would get in an accident would be (0.05)(0.2)+(0.15)(0.5)+(0.3)(0.3) = 0.175.

The probability that a person who has spent one year accident free is of a certain risk level n, letting Pn be the probability that a person is in an accident and N be the proportion of people in risk category n,

N(1 - Pn)/0.825