Question 20
The program of a subject consists of $n$ questions; The exam consists of developing one of those questions, chosen at random. A student only knows a question, but can repeat the $n$ exam times. Express, as a function of $n$, the probability $p_{n}$ for the student to pass the exam. Does $p_{n}$ grow or decrease by increasing $n$? Calculate $$
\lim_{n \rightarrow \infty} p_{n}
$$ What is the highest of the lower bounds of the probabilities $p_{n}$?
\lim_{n \rightarrow \infty} p_{n}
$$ What is the highest of the lower bounds of the probabilities $p_{n}$?