
Refer to the exhibit.
To predict whether or not a customer will renew their annual property insurance policy, an insurance company built and operationalized a naive Bayes classification model. In the model, there are two class labels, renewal and non-renewal, that are assigned to each customer based on their attributes.
A subset of the key attributes, their values, and corresponding conditional probabilities are provided in the exhibit.
A customer has the following attributes:
# Age is greater than 65 years
# Owns their own home
# Renewal month is August
If 20% of customers do not renew the police every year, what is the score for a renewal in the naive Bayesian model for the customer described above?
Correct Answer: D
The formula for Naive Bayes is:

For the renewal class, we are given:
# P(Class = Renewal) = 0.8 (since 80% renew the policy)
# P(Age > 65 years | Renewal) = 0.3
# P(Housing = Own | Renewal) = 0.9
# P(Renewal Month = August | Renewal) = 0.1
P(Renewal) = P(Renewal) × P(Age > 65 years | Renewal) × P(Housing = Own | Renewal) × P (Renewal Month = August | Renewal) P(Renewal) = 0.8 × 0.3 × 0.9 × 0.1 = 0.0216