A certain computer program randomly generates equation of line is form

I am responding to a pm from himanshuhpr.

First of all, I am intrigued by the solution of the very intelligent VeritasPrepKarishma, for whom I have considerable respect. Nevertheless, I beg to differ.

I believe there are some significant flaws in the question. First of all, the grammar is embarrassingly atrocious, but we'll let that pass. More to the point === we are told that the program "randomly" generates lines --- how exactly is this process randomized? For example, the line goes through P --- Are all slopes equally likely? Or are all angles equally likely? If we select P and a y-intercept, are all y-intercept equally likely? Are we randomly selecting one other point in the x-y plane, and all of those points are equally likely? Those are four different ways of specifying the probabilistic process, and I believe at least some of them give different numerical answer to the question. As soon as the thing you are specifying (here, a line) can be specified in a variety of ways, its not enough to say "random" --- you have to specify exactly how the selection process proceeds.

Because the question does not specify the details of the probabilistic selection process, I believe it is a fundamentally flawed question.

Does that make sense?

Mike