At a Tigers vs. Foxes football game in California, you observe that 70% of the fans are wearing Tiger T-shirts, 20% of the fans are wearing Foxes shirts, and 10% of the fans are not wearing either type of T-shirt. (Assume that no fan falls into more than one of these categories.) Furthermore, you psychically deduce that 50% of the fans wearing tigers T-shirts are currently students, 80% of the fans wearing foxes t shirts are currently students, and only 15% of fans wearing neither type of T-shirt are currently students. What is the probability that a randomly selected student at the game is wearing a tigers T-shirt? Round your answer to 4 decimal digits (if necessary). Show your work please step by step.