What is the meaning of "with probability at least 1-x over the drawing of the m training patterns"?

Question

I'm reading a book about Support vector machine and I encounters this ,so what is the meaning of $\text { with probability at least } 1-\delta \text { over the drawing of the m training patterns}$

Answer 1

Do the following (random) procedure:

1. Draw $m$ samples from the unknown underlying distribution $P$.
2. Train your model $f$ (SVM) on these $m$ points.

Now, with probability $1-\delta$ this procedure results in a model $f$ (which depends on your training data!) that has a misclassification probability bounded by (7.7).

Formally, denoting $y(x)$ for the correct label for any $x$: $$P_{x_1,\dots,x_m} \Big( P_x \big(f_{x_1,\dots,x_m}(x) \neq y(x) \big) \le (7.7) \Big) \ge 1-\delta$$