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Consider rolling a dice with probabilities for the outcomes of different states in the following two scenarios: a.) P(e1) = 1/6, P(e2) = 1/6, P(e3)

Consider rolling a dice with probabilities for the outcomes of different states in the following two scenarios:

a.) P(e1) = 1/6, P(e2) = 1/6, P(e3) = 1/6, P(e4) = 1/6, P(e5) = 1/6, P(e6) = 1/6

b.) P(e1) = 1/6, P(e2) = 1/6, P(e3) = 1/6, P(e4) = 1/6, P(e5) = 1/9, P(e6) = 2/9

Calculate the Shannon entropy for the two scenarios and determine which one has higher uncertainty.

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