Three companies A, B and C are competing for a contract to build a condominium. The probabilities that companies A, B and C will win the contract are 0.25, 0.45 and 0.3 respectively. if company A, B and C win the contract the probability that they will make profits are 0.8, 0.9 and 0.7 respectively.

i. Construct a tree diagram based on information given in the question.

ii. What is the probability that the companies will make profit?

iii. If the contract is found to be profitable, find the probability that the contract was given to company A