A problem with multiple uniformly distributed random variables

[geeknick]

Let's say we have n random variabes t that are drawn from uniform distributions. The lower boundary of all those distributions is 0, but each distribution has its own upper boundary B(n). That is: t(n) is drawn from the uniform distribution [0, B(n)].

1) What is the probability that in one trial t(1) is the smallest of all t?
1) What is the probability that in one trial t(1) is the greatest of all t?

I suppose this might be related to this thread: