In Sunnytown there are 6000 single-family houses, of which 2400 are equipped with a wood pellet heating system. Two thirds of the single-family houses with wood pellet heating have this combined with a solar thermal system. 50\% of all single-family houses are equipped with neither a wood pellet heating system nor a solar thermal system.

\textbf{(1a)} [3 marks] Create a completely filled four-field table for the described situation.

\textbf{(1b)} [2 marks] A randomly selected single-family house is equipped with a solar thermal system. What is the probability that it has a wood pellet heating system?

The tree diagram shown represents a two-stage random experiment with events $A$ and $B$ as well as their complementary events $\bar { A }$ and $\bar { B }$.\\
\textit{[Figure]}

\textbf{(2a)} [2 marks] Determine the value of $p$ so that event $B$ occurs in this random experiment with probability 0.3.

\textbf{(2b)} [3 marks] Determine the maximum possible value that the probability of $B$ can assume.

On a section of a lightly travelled country road, a maximum speed of 80 km/h is permitted. At one location on this section, the speed of passing cars is measured. In the following, only those journeys are considered where the drivers were able to choose their speed independently of one another.

For the first 200 recorded journeys, the following distribution was obtained after classification into speed classes:\\
\textit{[Figure]}

In 62\% of the 200 journeys, the driver was travelling alone, 65 of these solo drivers exceeded the speed limit. One journey is randomly selected from the 200 journeys.\\
The following events are considered:\\
$A$ : ``The driver was travelling alone.''\\
$S$ : ``The car was speeding.''\\