# Probability that some coefficients will be zero with lasso regression

Maybe it is duplicate, but I don't know how to ask a right question.

Suppose I fixed some lambda, for instance lambda = 1. I draw the usual "square" |x| + |y| = 1. Now I want to find probability, that if I will randomly choose a point and axes for gaussian (in some sense), than it will eventually touch the square in the corner.

Basically i'm interested in regions, starting from which i will make some of the coefficients zero...

Maybe i'm not clear?