Ordered Random Variables

Suppose \(X\) and \(Y\) are two random variable such that \(X \geq Y\).

1. For a fixed number \(T\), which would be greater, \(\mathbf{P}(X \leq T) \) or \(\mathbf{P}(Y \leq T) \).
2. What if \(T\) is a random variable ? (If it helps you think about the problem, assume \(T\) takes values in \(\{1,\cdots,n\}\). )