A data scientist aims to develop a neural network model to predict whether a customer will be interested in a new product. Each customer record contains the following attributes: Age $($ranges from $20$ to $70),$ Ethnicity $($possible values are White, Asian, Black, Hispanic, Others$),$ Annual Income $($ranges from $20000$ to $500000),$ Whether he$/$she is a new customer $($possible values are Yes. No$).,$ suppose the target variable can take binary values: 'Yes' means a customer will be interested in a new product; $\text{'}$No$\text{'}$ means the opposite. What is the CORRECT design of the output layer in a neural network model for the classification task?

$$a$)$ The output layer consists of $1$ output node, and one$-$hot encoding is needed on the target output variable.

$$b$)$ The output layer consists of $2$ output nodes, and one$-$hot encoding is needed on the target output variable.

$$c$)$ The output layer consists of $2$ output nodes, and no additional encoding is needed on the target output variable.

$$d$)$ The output layer consists of $1$ output node, and no additional encoding is needed on the target output variable.