Dice Probability

I thought this was a fun one, I hope you guys like it!

[mr.noname]

me confidently saying 50% in my head *they can be equal too* well then...

[cryptopeter]

Only YOU could get a 50 year old dude interested in fun math when i could be at the beach or eating bacon or at the dentist on NO2!! Love you man. Pete in Palm Beach

[DanielWalvin]

36 possibilities, take out the 6 cases where they're equal, leaving 30, then halve it because symmetry, to get 15.

[kangkongfan]

this one was a more simple and easier for me to understand problem, love it

[KarlSnyder-jhic]

Great prob, b/c the solution can be applied to a huge class of probs.
Makes me thoughtful

[AVeryCooIName]

Imma try this.
For n number rolled for red, There is always 1 way that's a draw, n-1 ways where red wins, and 6-n ways white wins. So if you iterate through each of the possible numbers red can roll and sum the results, there are 15 wins for red, 6 draws, and 15 wins for white. So 15/36 or 5/12

[claxviith]

Does solving your puzzles in the time of the short means i can one day hope to draw by typing equations in desmos?

[dr.mikelitoris]

Here’s another method: the probability that the two dices are equal is 1/6 as the second dice has to be whatever the first one is and has a 1/6 chance of doing so.

Thus there’s a 1-1/6=5/6 chance of the two dice not being equal. By symmetry, half of these have red bigger than white and the other half have white bigger than red. So the probability is 5/12

[danpliska]

i wonder if cool guy would have figured it out correctly?

[rndmname]

They are 36 different possibilities in total
6 of them are equal number we don't want we put them aside
So 30 possibilities are left.
And in everyone of these 30 possibilities one dice's number is greater than the other one
It's either red > white, or otherwise
So half of them are correct.
So in that 30 possibilities, 15 of them are correct.
15/36 (5/12) is the answer.

[froyocrew]

since the answer must be the same probability that white is greater than red due to no mention of special treatment, meaning white and red are independent, the only possible answer is 5/12 right off the bat. P(red greater than white) + P(equal) + P(red less than white) = 1 so 2 P(red greater than white) = 1 - 1/6

[critshot_]

Well, let me ask you a question. We have 3 identical dice. We throw all 3 of the dice at the same time. What is the probability of the situation where these dice are not the same?

[dacianbonta]

half of what is left after excluding equalities

[egg]

100%. The red die is on six and the white die is on four. The question never tells you to roll them. Alternatively, 0%, because there is exactly one red die and one white die. /j.

[dve]

6 red choices, 6 white choices, that's 12 total. 1 is too small to win so only 5 on the red can win.
5/12

[PopeVancis]

Ans is Σ(5, n=0)n/36, which is 15/36 which simplifies to 5/12

[MrPresident]

I just thought this: 1/6 probability they’ll be the same (0.167) so half of 1-0.1667 is 41.67% 🤷‍♂️

[Borne]

Isn't that the same chances for both die tho?

[jassmeet]

not a big math guy but if the table was reversed, wouldn’t the probability for red be 58.33%..?

[ralph]

How exciting? Let me rephrase
Exciting how?