I am doing some practice problems to prepare for my statistics exam, and I just want to know if my reasoning is correct on one problem, and if not, I want to know how I should reason through this. The question is as follows:
X, Y are random variables following the Beta distribution B(120, 2019). What is P(2X+4 > 3Y)?
My reasoning is that since X,Y are following the Beta distribution, any x,y $\in$ X,Y must be bound to the interval (0,1). Thus, 2X+4 must be bound to (4,6), while 3Y must be bound to (0,3). So would I be right in saying this probability is 100% since min(X)>max(Y)? Thank you for any help. Again, I am not just looking for the answer, I am looking to see if my reasoning is correct, and how I should reason through it if my reasoning is incorrect.