Problem 3 [20 pts (10,10)]: Step Right Up! You are given the chance to play a carnival game. You have 4 indistinguishable balls to throw into 4 colored pots. The pots are colored red, blue, green, and pink. You will throw each ball one at a time into these pots. However, you must play this game blindfolded. The game pays out as follows 0 $1 for each ball in the red pot 0 $2 for each ball in the blue pot 0 $3 for each ball in the green pot 0 $4 for each ball in the pink pot How much do you expect to win: i. Assuming every ball lands in some pot is equally likely to land in any pot? ii. Assuming every ball has a 1 in 3 chance of not landing in any pot (with no payout) but otherwise has an equally likely chance of landing in any pot