An actuary has done an analysis of all policies that cover two cars. 70% of the policies are of type A for both cars, and 30% of the policies are of type B for both cars. The number of claims on different cars across all policies are mutually independent. The distributions of the number of claims on a car are given in the following table.

Number of Claims Type A Type B
0 40% 25%
1 30% 25%
2 20% 25%
3 10% 25%
Four policies are selected at random. Calculate the probability that exactly one of the four policies has the same number of claims on both covered cars. The answer is 0.417. What are the steps to getting this answer?