thanks for the answer, regarding the question:

you have two variables a and b that are uniformly distributed between 0 and 1

a and b are independent of each other

you chose randomly a and b

what is the probability to chose a and b so that

a > b
3b > a

My suggestion:

a' = a/(a+b)
b' = 1-a'

3 > a'/(1-a') > 1

so that 3/4 > a' > 1/2

giving a probability of 25%... is that correct? is the transformation to a' possible? if so, how would you prove that?

ty