1. Between two games offered to you, would you rather (i) roll a die once and ge
ID: 3008240 • Letter: 1
Question
1. Between two games offered to you, would you rather (i) roll a die once and get paid $1 million for each dot on the upturned face, or (ii) roll a die one million times and get paid $1 times the number on the upturned face for each roll? Why? (Suppose that you are risk averse.)
2. If you roll 2 fair dice and add the points on each of the upturned face, what is the most likely sum? What is the probability of getting this sum? Hint: For rolling 2 dice, there are 6 × 6 = 36 possible outcomes. You can write all 36 possible outcomes and find sum for each outcome, then find the probabilities of the sums. Or, alternatively, the number of ways of getting a particular sum ‘s’ can be found by expanding the ‘generating function’ g = and extracting the coefficient of .
Explanation / Answer
2.
Possible sums: 2,3,4,5,6,7,8,9,10,11,12
P(2) = 1/36; P(3)= 2/36; P(4)=3/36; P(5)=4/36; P(6)=5/36; P(7)=6/36; P(8)=5/36; P(9)=4/36; P(10)=3/36; P(11)=2/36; P(12)=1/36
Hence most likely sum = 7
1. Highest money that can be won by (i) = $6 million
Lowest money that can be won by (i) = $1 million
In (i), probability of all 6 outcomes are equal.
i.e P(1) =1/6; P(2)=1/6; P(3)=1/6; P(4)=1/6; P(5)=1/6; P(6)=1/6
where P(n) is the Probability of getting n million dollars.
In case (ii) total possible outcomes = 6^1000000
Lowest money = $1 million.
P(1)=1 / 6^1000000
Highest money = $6 millions
P(6)= 1/6^1000000
If I am a risk averse person, I would choose option (i) because I know the risks and the probability of winning the highest money is higher in case (i). Also a risk averse person is happy with lower returns for known risks, rather than higher returns for unknown risks.
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