An organisation needs to select a building construction company to make houses in cities. Three companies X, Y and Z are short-listed with the probability of their selection being $\frac{1}{3}$, $\frac{2}{9}$ and $\frac{4}{9}$ respectively. It was found that there were $20%$, $40%$ and $30%$ chances respectively, of delivering poor construction quality. Based on the above information, answer the following questions : (i) If the building constructed was found to be strong, then what is the probability that the construction contract was given to the company X ? (ii) If a part of the newly constructed building falls off, then what is the probability that it was due to the selection of company Y or Z ?