**Naive Bayes Classifier Method**

Here, we want to classify a **Homeowner = Yes, Status = Employed, Income = Average** and predict the *class label* for this sample.

- The above sample dataset does not contain the class label for this sample.
- Hence, by using
**Naïve Bayes Classifier** we can find out the class table value for the given sample.
- To do this we need to calculate the below probabilities:

First, calculates the Probabilities for $P(x | Yes)$

$$P(Yes) = \frac{3}{10} $$

$$ P(Homeowner = Yes│Yes) = \frac{0}{3} = 0 $$

$$ P(Status = Employed│Yes) = \frac{1}{3} $$

$$ P(Income = Average│Yes) = \frac{3}{3} = 1 $$

Second, calculates the Probabilities for $P(x | No)$

$$P(No) = \frac{7}{10}$$

$$P(Homeowner = Yes│No) = \frac{3}{7}$$

$$P(Status = Employed│No) = \frac{3}{7}$$

$$P(Income = Average │No) = \frac{1}{7}$$

According to Naïve Bayes Classifier

$$P(C│X)=P(x1│C) × P(x2│C) ×…………P(xn│C) × P(C)$$

Therefore, Probability for Class label value *Yes* we have

$$Yes = P(X│Yes) × P(Yes)$$

$$Yes = P(Homeowner = Yes│Yes) × P(Status = Employed│Yes) × P(Income = Average│Yes) × P(Yes)$$

$$= 0 ×\frac{1}{3} × 1 × \frac{3}{10} = 0$$

*If one of the conditional probabilities is zero, then the entire expression becomes zero.** This can be seen in the above scenario.*

Therefore, Probability for Class label *No* we have

$$ No =P(X│No) × P(No)$$

$$No = P(Homeowner = Yes│No) × P(Status = Employed│No) × P(Income = Average │No) × P(No)$$

$$= \frac{3}{7} × \frac{3}{7} × \frac{1}{7} × \frac{7}{10} = 0.018$$

As

$$P(X│No).P(No) \gt P(X│Yes).P(Yes)$$

$$because,\ 0.018 \gt 0$$

*Therefore, this sample ***(Homeowner = Yes, Status = Employed, Income = Average)** gets classified under Class label **’No’.**