Advantech is a global developer of state-of-the-art battery designs for use in electric vehicles. In light of the demand for new products, AT is considering investing in research and development for a new line of solid-state batteries. The company estimates that there is only a 65% chance that the new product will be successful, and therefore, a 35% chance it will not be. If it is successful, the increase in corporate profits will be $3.8 million. If it is not successful, the loss will be $2.9 million. The company can decide whether to go ahead with the research and development on this product, or not. Set up a payoff table and prepare the expected payoffs in millions (2 marks). Before deciding whether to proceed, or not, a marketing survey can be conducted at a cost of $80,000 to offer greater accuracy as to whether the product will be a success, or not?
Based on past performance, successful products were predicted by a survey to be successful 82% of the time, whereas unsuccessful products were predicted to be unsuccessful 79% of the time. If the marketing survey is conducted, prepare the posterior probabilities of the respective states of nature for each of the two possible predictions from the market survey.