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For **smooth**, there are 4 positive examples and 1 negative, so the entropy
is -(4/5)×log_{2}(4/5) - (1/5)×log_{2}(1/5)
which is about 0.7219.

(Again, in the exam, you would leave this as an unevaluated expression.)

For **wavy** there is one positive and one negative example, so the
entropy is -(1/2)×log_{2}(1/2) - (1/2)×log_{2}(1/2) = 1.

(I *would* expect you to know that log_{2}(1/2) = –1,
and so evaluate this expression.)

For **rough** there are two positive and two negative examples, so the
entropy is -(1/2)×log_{2}(1/2) - (1/2)×log_{2}(1/2) = 1.

Expected information for a split on texture is thus:

Expected information gain for a split on texture is thus 0.94566 - 0.8736 = 0.07206.