Logistic regression

Let's say that you have weights for a logistic regression model $\vec{w}=(0.8, 4, -3)$ and one observation $\vec{x}=(10, -2, 0.2 )$. The set of class labels is $0$, which means cat, and $1$, which means dog.

The logistic function has the following parameters: $L = 1, k=2, x_0=0$. The cut-off point equals $0.5$.

Your task is to predict the class label of the given observation. As an answer provide the probability of belonging to that class (either $Pr(y=0|\vec{x})$, or $Pr(y=1|\vec{x})$. Round the answer to the second decimal place. For example, if your answer is $0.3479$, you write $0.35$.

Tip: Recall the logistic function $f(x) = \frac{L}{1+e^{-k(x-x_0)}}$ and the fact that substituting $\vec{x}$ into $f(x)$ returns the probability of belonging to class $1$. The probability of belonging to class 0 is 1 - the probability of belonging to class $1$.