A survey of MBA students reveals that among GMAT scorers above 750,52% took a preparatory course, whereas among GMAT scorers of less than 750 only 23% took a preparatory course. An applicant to an MBA program has determined that he needs a score of more than 750 to get into a top 20MBA program, but he feels that his probability of getting that high a score is quite low −20%. He is considering taking a preparatory course that costs only $50. He is willing to do so only if his probability of achieving 750 or more doubles. Draw the probability tree. What should he do - spend $50 or not?