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For smooth, there are 4 positive examples and 1 negative, so the entropy is -(4/5)×log2(4/5) - (1/5)×log2(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)×log2(1/2) - (1/2)×log2(1/2) = 1.

(I would expect you to know that log2(1/2) = –1, and so evaluate this expression.)

For rough there are two positive and two negative examples, so the entropy is -(1/2)×log2(1/2) - (1/2)×log2(1/2) = 1.

Expected information for a split on texture is thus:

0.7219×(5/11) + 1×(2/11) + 1×(4/11) = 0.8736

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