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 • $1 for each ball in the red pot • $2 for each ball in the blue pot • $3 for each ball in the green pot • $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?
Discrete Mathematics
Problem 3
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
• $1 for each ball in the red pot
• $2 for each ball in the blue pot
• $3 for each ball in the green pot
• $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?
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