Strike It Rich Is a Gold Mining Company That Is

Strike It Rich is a gold mining company that is attempting to decide whether to invest in a particular site.The probability that the site has gold is 0.50.In order to obtain more information about the potential presence of gold,the company has hired a geologist to analyze the soil.Past history indicates that there is a 60% chance that the geologist's test is positive given the presence of gold and a 35% chance that the test is positive given the absence of any gold.What is the probability of the presence of gold given that the geologist's test yielded a positive result? Use Bayes' theorem to compute this posterior probability.