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 Apr 16, 2019
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\(\text{The distribution of a single spin is}\\ P[\{3,4,6\}] = \left\{\dfrac 1 2,\dfrac 1 4, \dfrac 1 4\right\}\)

\(\text{The distribution of the sum of 2 spins is }\\ P[\{6,7,8,9,10,12\}]=\left\{\dfrac 1 4,\dfrac 1 4,\dfrac{1}{16},\dfrac 1 4, \dfrac 1 8,\dfrac{1}{16}\right\}\)

 

\(\text{We want the distribution of the vacation choice to be "fair",}\\ \text{ i.e. discrete uniform with }n=4\\ \text{It's seen that choice 3 accomplishes this}\)

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 Apr 16, 2019

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