random Mathematics(probability) question.

[Howler Dagger]

My question is, what is the chance of rolling a pair on 3d4 vs. 2d4?

[Astrella]

Does three of a kind fall under a pair or not?

[Howler Dagger]

yes
blablabla

[Haruki-kun]

The probability of rolling a pair in 2d4 is 1/4. 4*4 = 16, which is the total possibilities in rolling 2d4. And there's 4 possible pairs. So 4/16, which is 1/4

The possibility when rolling 3d4: there are 64 different possibilities. The pairs in that are: 111, 112, 113, 114, 121, 131, 141, 211, 311, 411. Multiplied by 4, for each of the numbers that can be paired.

40/64

Unless you don't count three of a kind. In which case: 112, 113, 114, 121, 131, 141, 211, 311, 411 multiplied by 4, 36/64.

Credit to Reinholdt for helping me out with this.

[Gardener]

on 2d4: (1, 1), (2, 2), (3, 3) and (4, 4) are the four acceptable points in a 16-point evenly distributed possibility space, which means a probability of 4/16 or 1/4.

On 3d4: Rolling a pair is the same as not rolling three distinct numbers.

By the above, there is a 1/4 chance the two rolls are the same. Thus, there is a 3/4 chance that they are not.
Given that the previous two rolls were distinct, the third has a 1/2 chance of being distinct, as there are two numbers showing.

Thus, the probability that there are no pairs on 3d4 is (3/4*1/2) = 3/8, so the chance of pairs is 5/8. If you want to exclude triples, subtract another 1/16 (four triples in a uniform 64-point space).

EDIT: Swordsaged

[Howler Dagger]

so the final answer is 1/4 vs. 5/8? thanks.