Buffon's cross

Hi,
I need some help in the attached problem,Q2.My difficulty is not with the probability part ,rather,with determination of the geometric conditions for for each number of crosses.

Hey hedi.

This looks like a frequency problem where the smaller the distance between lines, the higher the probability.

Once the needle length is the same as the distance between lines the probability will be 1 from there on in.

But in terms of when this is less it should be proportional to the ratio of the needle size to that of the distance between the lines if you assume that every possible placement has the same probability (uniform probability).

I need the second question,this with the cross.For computing the expectancy i need to compute the probability distribution of z,and i need help with that.

What are the ranges of the cross elements? Are they always less than the distance between parallel lines?

The cross is made of two unit needles.

And they can be positioned absolutely anywhere as long as they are axis aligned?