Three car brands A, B, and C have all the market share in a certain city. Brand A has 20% of the market share, brand B has 30%, and brand C has 50%. The probability that a brand A car needs a major repair during the first year of purchase is 0.05, the probability that a brand B car needs a major repair during the first year of purchase is 0.10, and the probability that a brand C car needs a major repair during the first year of purchase is 0.15.
a. What is the probability that a randomly selected car in the city needs a major repair during its first year of purchase?
b. If a car in the city needs a major repair during its first year of purchase, what is the probability that it is a brand A car?