Wie hoch ist die Wahrscheinlichkeit dass man eine 6 auf dem Zeugnis bekommt wenn man 2 mal in der Mathearbeit eine 6 geschrieben hat aber trotzdem mitarbeitet?

Hmm, probability bill. Suppose the written and oral note have the same weighting, then you need an average of 5.5 to get another 5. That means your oral note should be better than 5. Depending on how exactly your teacher is, a 5+ or a 4-5 could be enough. The value range 1-4.5 comprises 3.5 values. The value range 4,5-6 includes 1.5 values.

The computational probability that you get a 6 is therefore 1.5 to 3.5 or different: 1.5 out of 5, that is 30%. However, the probability applies only if all oral notes are equally likely. If you have written a six twice, it is rather unlikely that your oral note is in the range 1-3.5. If you clip out the area, your chance to get a 6 to 1.5 from 2.5, so 60%.