Calculating Probability for X from f(x;θ) with θ > 0

[safina]

Let X be a single observation from the density $$f\left(x;\theta\right) = \theta x^{\theta -1}I_{(0,1)} (x)$$, where $$\theta > 0$$. What is the $$P\left[X \geq \frac{1}{2} |\theta > 1|\right]$$?

Please help me structure the solution of this problem

 

[statdad]

Let X be a single observation from the density $$f\left(x;\theta\right) = \theta x^{\theta -1}I_{(0,1)} (x)$$, where $$\theta > 0$$. What is the $$P\left[X \geq \frac{1}{2} |\theta > 1|\right]$$?

Please help me structure the solution of this problem

What do you mean by

$$P\Big(X \ge \frac 1 2 |\theta > 1 |\Big)$$