Discuss the below:
In your opinion, the best outcome would be to have the communications contract awarded to your company but to have the construction contract awarded to a different company. This is not because you are fond of your competition, but instead because if you were to win both, the result would place some strain on your (relatively) small firm's resources. Of course, if the construction contract were the only one you received, it would be good for the firm. You have placed subjective probabilities of 0.60 and 0.45 on the communications and construction contracts respectively, and believe that these events may be considered statistically independent for the purpose of these calculations.
Find the probability that the result is your best outcome.
Given that you are awarded at least one contract, find the conditional probability that (in particular) you are awarded the communications contract. This may not be as straightforward as it might appear.