Consider a binary classification problem with three input features $(x_1,x_2,x_3)$ and bi$-$

nary outputs yin$\{0,1\}.$ After training a Logistic Regression model on a training

dataset, one obtains the following optimal parameters:

hat$()=(-2,1\mathrm{.}5,2,1)$

According to the model, the probability that a particular triple $u=(x_1,x_2,x_3)$ belongs

to class $y=1$ is $0\mathrm{.}65.$

$($i$)$ What is the probability that the input $u^{\text{'}}=(x_1,x_2+1,x_3)$ is classified as $y=1?$

$($ii$)$ Find the odds ratio that the input $u^{\text{'}\text{'}}=(x_1,x_2,x_3-1)$ belongs to class $y=1?$