How to calculate the class probabilities and classify using Naive Bayes classifier?

Question

We have data on 1000 pieces of fruit. The fruit being a Banana, Orange or some Other fruit and imagine we know 3 features of each fruit, whether it’s long or not, sweet or not and yellow or not, as displayed in the table below:

A piece of an unknown fruit with these features are provided: Long, Sweet and Yellow. 

Calculate probability of each of these 3 classes based on Naive Bayes Classification algorithm and report the class.

Answer 1

You can see the step-by-step solution for this question here. The solution can include Laplace Smoothing as well, but the result will not change. For Laplace smoothing, 1 should be added to the numerator of probability and in the denominator, you should add the number of unique features (Long, Sweet, Yellow are unique features, therefore 3 should be added in the denominators).

Comments

How come we don't apply Laplace smoothing to this question? In this question, P(Orange | Long, Sweet, Yellow) = 0 since P(Long|Orange) = 0, so doesn't that mean we need to apply Laplace smoothing to not lose the affect of the probability of the rest of the features?

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We can apply Laplace smoothing, still will not affect the result.... it will definitely affect if have  1 more feature which make Banana probability Zero... i.e. RED colour... in that case we dont have any other solution but to apply Laplace smoothing