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Eine 6 würfeln

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/eine-6-wurfeln/

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Solution

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Exercise:
Wie oft muss ein fairer Würfel mindestens geworfen werden damit man mit über % Wahrscheinlichekeit mindestens einmal eine gewürfelt hat?

Solution:
Die Wahrscheinlichkeit nach n Würfen eine gewürfelt zu haben setzt sich zusammen aus der Wahrscheinlichkeit im ersten Wurf eine gewürfelt zu haben oder im ersten keine aber im zweiten Wurf eine gehabt zu haben oder in den ersten beiden Würfen keine aber im dritten Wurf eine etc... Formal heisst das für n Würfe: p_n p_hitdots + p_misshitdots + p_missmisshitdots + dots frac + frac frac + fracfrac frac + dots frac + frac leftfracright^ + frac leftfracright^ + dots + frac leftfracright^n- frac left + leftfracright^ + leftfracright^ + dots + leftfracright^n- right Die dabei zu erkenne geometrische Reihe kann formal vereinfacht werden: s_n- + leftfracright^ + leftfracright^ + dots + leftfracright^n- _k^n- q^k frac-q^n-q Nun findet man einfach: p_n frac frac-q^n-q && textmit qfrac Für den vorliegen Fall errechnet man für n: . &stackrel!le p_n &le frac frac-q^n-frac &le -q^n q^n &le -. log_qq^n &ge log_q. n &ge log_q. fraclog.logq &ge . Nach Würfen hat man also mit über % Wahrscheinlichkeit eine gewürfelt.

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Contained in these collections:

Wahrscheinlichkeitsrechnung by uz

19 | 19

Attributes & Decorations

Tags	mathematik, statistik, stochastik, wahrscheinlichkeit, würfel, würfeln
Content image
Difficulty	(2, default)
Points	2 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
Decoration
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Link