A wheel of fortune consists of five equally sized sectors. One of the sectors is labeled "0", one is labeled "1" and one is labeled "2"; the other two sectors are labeled "9".

\textbf{(1a)} [2 marks] The wheel of fortune is spun four times. Calculate the probability that the numbers 2, 0, 1 and 9 are obtained in the specified order.

\textbf{(1b)} [3 marks] The wheel of fortune is spun twice. Determine the probability that the sum of the numbers obtained is at least 11.

\textbf{(2)} [3 marks] The random variable $X$ can only take the values 1, 4, 9 and 16.\\
It is known that $P ( X = 9 ) = 0.2$ and $P ( X = 16 ) = 0.1$ as well as the expected value $E ( X ) = 5$. Using an approach for the expected value, determine the probabilities $P ( X = 1 )$ and $P ( X = 4 )$.

\textbf{(3)} [2 marks] Given is a Bernoulli chain with length $n$ and success probability $p$. Explain that for all $k \in \{ 0 ; 1 ; 2 ; \ldots ; n \}$ the relationship $B ( n ; p ; k ) = B ( n ; 1 - p ; n - k )$ holds.

A company organizes trips with an excursion ship that has space for 60 passengers.