After graduation your first job is with Abibas Inc., a company that specializes in sportswear with collegiate logos. To improve profits the company wants to introduce a new selection of sportswear. The company will choose either the UNC-CH or NC STATE logo. The marketing department's research shows that the odds are 96 to 1 that the new sportswear based on the UNC-CH logo will be profitable, while the odds are only 24 to 1 that the new sportswear based on the NC STATE logo will be profitable. Therefore the marketing department concludes that the UNC-CH logo is the overwhelming favorite. The marketing department also says that since 96 = 4*24, the company should spend 4 times as much money developing the UNC-CH sportswear than it would spend developing the NC STATE sportswear. You claim that the situation is not as overwhelming as it appears and that spending that much more on the UNC-CH logo would be a mistake. Required:
a. Calculate the probability that the new sportswear based on the UNC-CH logo will be profitable.
b. Calculate the probability that the new sportswear based on the NCSTATE logo will be profitable.