A group of law professionals is considering constructing a law firm. If the demand for the firm is high, then the law pr

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A group of law professionals is considering constructing a law
firm. If the demand for the firm is high, then the law
professionals can realize a net profit of $120,000. If the demand
is low, then they could lose $47,000. Of course, they don’t have to
proceed at all, in which case there is no cost. In the
absence of any market data, the best these law professionals can
guess is that there is a 56% chance that demand will be high.
The law professionals have been approached by a market research
firm that offers to perform a study of the market. The market
researchers’ past records show that among the high demand market,
59% show a positive result in the study. Among the low demand
market, 73% show a negative result.
What is the probability that the demand is high given that the
study shows a positive result? (Enter 0.53 for 53%)