Problem 3. A gacha/capsule machine costs $1 to use and produces a single random prize per use. Any random prize from the machine has an 8% chance of containing a super-rare action figure. The random prize contents are independent of each other (since the prize capsules are manufactured independent of each other) and the machine never runs out of prizes. a) Mei decides she is going to spend exactly $10 on the gacha, what is the probability of her acquiring a super-rare action figure (i.e., at least one) from her $10 investment? (4pts) b) Hiyori played the gacha and said she didn't get a super-rare action figure until she had spent $15. What is the probability of doing at least as poorly as Hiyori? (4pts) c) Kanako says she will spend exactly $100 regardless of how many super-rare action figures she gets. What is the expected number of super-rare action figures Kanako will acquire? What is the standard deviation? (4pts)