The image you uploaded is a German mathematics exam focused on probability and statistics. Here's an overview of the questions:

1. Task a): You're asked to determine the probability of certain events (random selection of households) based on a table showing the distribution of households in Germany in 2013. Specifically, you are tasked with calculating the probabilities of:

   • A randomly selected household being a 1-person household.
   • At least half of the selected households being multi-person households.
   • No 4-person households being chosen from the selected sample.

2. Task b): The question requires you to find the minimum number of households that must be selected randomly so that the probability of selecting at least 20% 2-person households is at least 95%.

3. Task c): Given the total population in Germany (80 million people in 2013), you are asked to estimate the total number of households in Germany.

4. Task d): The question involves hypothesis testing, where you test the null hypothesis that the proportion of 1-person households is 40.5%. The procedure involves using a sample size of 500 households and performing a significance test at a 5% significance level.

Would you like a detailed explanation or help solving any of these questions step by step?