Nivea Nandakumar has offered John Morgan an opportunity to finance Nivea's new high-technology company. But Morgan recognizes that other specialist bankers may have much more expertise in this technology, and he does not know what they would think about Nivea's chances of making this company succeed. From Morgan's perspective, the probability of Nivea's success that would be assessed by a specialist banker is an unknown quantity. Morgan first thought that if he could assume Nivea has not already approached any other banker, then this unknown quantity should have a Beta distribution with mean 0.45 and standard deviation 0.25. But Morgan had to recognize the possibility that Nivea might have already approached such a specialist banker. If she did, then the specialist banker must have thought the probability of Nivea's success to be below 0.4, because otherwise he would have already financed the company and so Nivea would not have approached Morgan. Morgan figured that a woman in Nivea's position would be equally likely to bring such an investment opportunity to Morgan first, or to a specialist banker first.

.(a)What would be the conditional probability of Nivea's success, if we were given that Nivea had already approached a specialist banker who then refused to finance Nivea's company?

.(b)Given only that Nivea has approached Morgan for financing, estimate the probability that Nivea previously approached a specialist banker and failed to get financing.

(c)In this situation, knowing only that Nivea has approached Morgan for financing, what should Morgan think is the probability of Nivea's success?