formula in DataScience book

Question

$$P(y^i = 1 | x^i)$$

Can't remember from book what's mean this P? Someone can help me?

book: "applied deep learning: a case-based approach to understanding deep neural networks"

Answer 1

Given $x^i$, it is the probability that $y^i$ takes value $1$.

Sometimes we write it as $Pr(y^i=1|x^i)$ as well.

Answer 2

The notation $P(y^i = 1 ~|~ \mathbf{x}^i)$ denotes the probability that the $i$'th example with feature vector $\mathbf{x}^i$ belongs to class 1, as opposed to class 0 (or some other class $k\not= 1$ if it's a multiway classification problem).