We flip a a biased coin 100 times.

p=probability of head

q=1-p= probability of tail.

Let us call the longest run of heads LH and the longest run of tails LT.

We define a random variable X=min(LT,LH) and Y=LH+LT.

What are the probability laws of X and Y?

Thank you for any help.

Ps : It is not a homework.