Suppose a studio manager is thinking about whether or not to produce a movie $($movie X$).$ A movie can become a $$blockbuster$,$ which will generate a net profit of $$10$M$,$ or it can become a $$failure$,$ in which case it will generate a loss of $$4$M$.$ The studio manager estimates that movie X has a $50-50$ chance of becoming a blockbuster or a failure. Now a marketing research company offers to provide a research service that allows the studio to know in advance whether movie X will be a $$blockbuster$$ or a $$failure$.$ There is $50\%$ probability that the research company says that the movie is a $$blockbuster$$ and $50\%$ probability that the research company says that the movie is a $$failure$.$ How much $($in terms of $$)$ is this marketing research service worth to the studio?