Case Study - 3 Two persons are competing for a position on the Managing Committee of an organisation. The probabilities that the first and the second person will be appointed are $0\cdot5$ and $0\cdot6$ respectively. Also, if the first person gets appointed, then the probability of introducing waste treatment plant is $0\cdot7$ and the corresponding probability is $0\cdot4$, if the second person gets appointed. Based on the above information, answer the following questions : (i) What is the probability that the waste treatment plant is introduced ? (ii) After the selection, if the waste treatment plant is introduced, what is the probability that the first person had introduced it ?