Problem 3 [15 pts]: Pirate's Life Captain Mosca is leading a pirate across the seas. You were chosen to be their rst-mate and together you have been on many an adventure. You have secured a lot of jewels for their collection. Their collection is broken into 3 chests Chest 1 contains the following 13 rubies 12 sapphires 8 emeralds Chest 2 contains the following 20 rubies 3 emeralds Chest 3 contains the following i. ii. 13 sapphires 10 emeralds Someone comes aboard asking for jewels. Captain Mosca wants to have them choose from a chest at random and then pick a jewel at random. The guest must do this 3 times without returning the jewel t0 the chest. At the end, the guest keeps what they grabbed. The captain asks you what this guest's haul will be at the end of the game. On average, how many rubies and emeralds did this person get? Suppose some sailor walks aboard. Captain Mosca decides to have them to choose a chest after rolling a 3-sided die and retrieve a sapphire. 'Ii'ue to pirate fashion, the die is unfair! The die is comes up as a 2 four times as often as any other number on the die. It get worse! The sailor has to keep trying, putting the jewel back and re-rolling the die, until they get a sapphire. The sailor comes to you asking how bad this game could be. On average, how many times does this sailor have to repeat this task until they get a sapphire