The question I have on hand is as follows :
We draw at random a number in interval [0,1] such that each number is "equally likely". Suppose we do the experiment two times (independently), giving us two numbers in [0,1]. What is the probability that the sum of these numbers is greater than 1/2?
My understanding is that since the experiments are independent, I am able to multiply the probability of each experiment with each other directly.
My attempt at this was to calculate probability of each experiment where x (the random number) is less than 1/4, thus giving me the probability of 1/16 when I multiply them. This would imply that there is a 15/16 chance my sum is greater than 1/2. However the answer is wrong since it is supposed to be 7/8.
Any help please? Thank you