I will first enuntiate the question and then explain what I'm not understanding.
Suppose $ X_1, X_2,\ldots, X_n $ iid with common distribution $ U(0,\theta)$. Define $M$ as follows:
$ M : =\max\{ X_1, X_2,\ldots, X_n \} $
Evaluate : $\Pr\left( M\leq \frac{\theta }{2} \right ) $
So, i have $ n $ random variables that are independent and identically distributed; I have a another random variable that will yield the maximum value of the mentioned sequence of random variables and then i have to evaluate the probability that this random variable is 'bounded' by $\theta$ divided by two. I understand all this informations separately, but i don't know how to connect them. How in the world, the fact that I know that they are iid and have a uniform distribution with a parameter $ a = 0 $ and $ b = \theta $ will help me finding out the probability of $M$? How even would I know what's the maximum value of the sequence? Thanks!
Hint: The probability that $M\leq \theta/2$ is the same as the probability that all $X_i$s are less than $\theta/2$.