2. Dr. Inks Weet, the head of the newly created Ministry of Silly Games, invents a new game called Canadian Roulette. The game works as follows: Four opaque bottles are obtained. One bottle is filled with water, and the other bottles all are filled with maple syrup. The bottles are put into a random order (the probability of any permutation is equal). Player A drinks the first bottle, Player B drinks the second bottle, Player A drinks the third bottle, and finally Player B drinks the fourth bottle. For each bottle of maple syrup a player drinks, that player collects a reward of 10 units of happiness. If a player drinks a bottle of water, that player collects a negative reward of -20 units of happiness. For example, a player that drinks a bottle of maple syrup and a bottle of water collects a total reward of 10- 20 = -10. (a) What is the expected reward for the second player? Explain your answer.

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What is the expected reward for the second player in both cases explained?

2.
Dr. Inks Weet, the head of the newly created Ministry of Silly Games, invents
a new game called Canadian Roulette. The game works as follows:
Four opaque bottles are obtained. One bottle is filled with water, and the
other bottles all are filled with maple syrup. The bottles are put into a random
order (the probability of any permutation is equal). Player A drinks the first
bottle, Player B drinks the second bottle, Player A drinks the third bottle,
and finally Player B drinks the fourth bottle. For each bottle of maple syrup
a player drinks, that player collects a reward of 10 units of happiness. If a
player drinks a bottle of water, that player collects a negative reward of -20
units of happiness. For example, a player that drinks a bottle of maple syrup
and a bottle of water collects a total reward of 10 – 20 =-10.
(a) What is the expected reward for the second player? Explain your answer.
(b) Suppose that the second player has observed that the first bottle contains maple
syrup. With this knowledge, what is the expected reward for the second player?
Explain your answer.
Transcribed Image Text:2. Dr. Inks Weet, the head of the newly created Ministry of Silly Games, invents a new game called Canadian Roulette. The game works as follows: Four opaque bottles are obtained. One bottle is filled with water, and the other bottles all are filled with maple syrup. The bottles are put into a random order (the probability of any permutation is equal). Player A drinks the first bottle, Player B drinks the second bottle, Player A drinks the third bottle, and finally Player B drinks the fourth bottle. For each bottle of maple syrup a player drinks, that player collects a reward of 10 units of happiness. If a player drinks a bottle of water, that player collects a negative reward of -20 units of happiness. For example, a player that drinks a bottle of maple syrup and a bottle of water collects a total reward of 10 – 20 =-10. (a) What is the expected reward for the second player? Explain your answer. (b) Suppose that the second player has observed that the first bottle contains maple syrup. With this knowledge, what is the expected reward for the second player? Explain your answer.
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