Three persons $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ apply for a job of manager in a private company. Chances of their selection are in the ratio $1:2:4$. The probability that $\mathit{A},\mathit{B}$ and $\mathrm{C}$ can introduce changes to increase the profits of a company are $0.8,0.5$ and 0.3 respectively. If increase in the profit does not take place, find the probability that it is due to the appointment of A.