Naive Bayes Example

We are trying to determine if its time to PlayTennis given that \[\langle Outlook=sunny, Temp=cool, Humid=high, Wind=strong \rangle \]
We want to compute \[ v_{NB} = \argmax_{v_{j} \in V} P(v_{j}) \prod_{i} P(a_{i} \,|\, v_{j}) \]
Given this set of examples we can calculate that \[ P(PlayTennis = yes) = \frac{9}{14} = .64 \] \[ P(PlayTennis = no) = \frac{5}{14} = .36 \] similarly \[P(Wind = strong \,|\, PlayTennis = yes) = \frac{3}{9} = .33 \] \[P(Wind = strong \,|\, PlayTennis = no) = \frac{3}{5} = .6 \] using these and few more similar probabilities we can calculate \[P(yes) \cdot P(Outlook=sunny \,|\, yes)\cdot P(Temperature = cool \,|\, yes)\cdot P(Humidity = high \,|\, yes)\cdot P(Wind = strong \,|\, yes) = .005 \] \[P(no)\cdot P(Outlook=sunny \,|\, no)\cdot P(Temperature = cool \,|\, no)\cdot P(Humidity = high \,|\, no)\cdot P(Wind = strong \,|\, no) = .021 \]
So \[ v_{NB} = no \]