The Probability of the Other Class

A binary classifier's final linear layer produces a single raw logit

$z = \mathbf{w} \cdot \mathbf{x} + b$

For one input the network has $\mathbf{w} = [\,3.0,\; -2.0\,]$, $\mathbf{x} = [\,1.0,\; 2.0\,]$ and $b = -0.3863$.

The logit is squashed by the sigmoid

$\sigma(z) = \frac{1}{1 + e^{-z}}$

whose output $\hat{y}$ is the Bernoulli parameter of the positive class.

What probability does this model assign to the negative class, $P(Y = 0 \mid X)$?

You may use $e^{1.3863} \approx 4.000$.