Wie hoch ist die Wahrscheinlichkeit beim Würfeln?

Wie hoch ist die Wahrscheinlichkeit bei 3 Würfen 2 Zahlen außer 6 doppelt zu haben.

Ich habe als Ergebnis 13,9% aber glaube es ist Falsch

Also akzeptable Ergebnisse sind zum Beispiel:

6,5,5

1,3,3

5,4,5

Und wie hoch ist die Wahrscheinlichkeit, dass keine Zahl doppelt vorkommt. (Mein Ergenis = 55,6%)

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Rhenane
1 year ago

There are a total of 63=216 possible results for triple cubes.

Results with double eye number, i.e. 11x, with x≠1 gives 6*5=30 possibilities: 6 for the 6 possible numbers can be double (11,22, etc.), 5 for number of possibilities for the 3rd number (i.e. the x). This has to be multiplied by 3 for the number of possibilities of each of these dice configurations (ddx, dxd, xdd), making 90 possibilities.

It is necessary to remove 5*3=15 because 66x, 6×6, x66 should be excluded. So p=75/216=25/216.

no number double: for the first there are 6 possibilities for the second then 5 and for the third 4. So p=120/216=5/9, i.e. your result fits here.

(For all 3 numbers to be equal (= last possible variant), there are 6 options, so you can also come (to control) to all options: 6+75+120+15=216)

eterneladam
1 year ago
Reply to  Rhenane

6*3=18 must be removed from this,

From your lead, I’d take 5*3=15…

Rhenane
1 year ago
Reply to  eterneladam

Right, of course: half 3 nights is probably not the best time for concentrated thinking… 🙂

p=75/216=25/72 instead of 72/216

Thanks for correcting – will change the numbers in my answer accordingly!