Let U=R. Let S be a well defined sample space. it is the case that there exists an event E such that Pr(E)=1/2
Do i just make up a sample space and event that satisfies the Pr(E) = 1/2 ?
What are U and R ?
What is the exact question : "is it the case that there exists an event E such that Pr(E)=1/2 ?" or is it a statement that you need to prove ?
Because you can consider a random variable X such that P(X=0)=1, that would make a counterexample.