The questions-not-worth-their-own-thread question thread IV

[Ziggy Stardust]

Math again ...

The chance to roll any double with two ten-sided dice is 10%. How does the chance to get a double (not triple etc) increase as you add ten-sided dice? If you roll three or four, what's the chance any two of them will show the same number?

Well after you roll the first dice:

2 dice, one out of 10 possible rolls of the second dice is a hit, indeed 10%

3 dice, out of 100 combinations: 10 - 1 combinations work when the second dice makes a double (the minus one is the combination where the third hits as well) and 10 - 1 combinations work for the third dice to make a double. 18 combinations out of a 100 = 18%

4 dice, out of a 1000 combinations: 100 - 10 - 9 work when second, third or forth dice hit. When any of the dice hit, the other two dices may not hit. There are 19 ways to hit with two dice.

3 times 81 = 243 working combinations = 24.3%





I think ... (having a bit of a hangover)

 

[Atticus]

Chances to get double or triple with three dice:

We do this by calculating the chances that no two dice show the same number. So first you cast one die, and it shows, let's say n. Then you cast another one, and it shows k. The chances for "k is not n" are 9/10. If k is not n you'll cast the third one, and the chances for it being not n nor k are 8/10.

So the chances for you getting three totally different numbers are 9/10*8/10 =72/100.

Now the rest 28/100 must be the probability for double or triple (because all the possibilities are double, triple and three different numbers). Because probability for triple is 1/10*1/10=1/100, the probability for "double, not triple" are 28/100- 1/100=27/100.

Chances to get double (or triple or four of the same) with four dice:

Like above chances for getting four totally different numbers are 9/19*8/10*7/10= 504/1000. (fractions on the left side are the probabilities of 2nd, third and fourth dice landing on a number that hasn't been cast before). So the chances for double, triple or four of the kind are 496/1000.

Notice that in this case you have to be more precise if you want to exclude "better" results than doubles, because there are possibilities of trips, four of the sama number and two pair.

That kind of exclusion calls for more calculations, and I leave it to you, as you've got an example already.

 

[Ziggy Stardust]

Ow shoot, I totally disregarded the second and third dice being the same.

 

[Atticus]

If you have hangover, you cannot be blamed.

 

[Mesousa]

Excellent. Thanks, both of you.

 

[Atticus]

No problem. I have to add that the cases of two pair and trips for four dice are little bit more difficult: For example in case of trips, you must take into account what die isn't part of it (four possibilities).

In the case of two pair you can choose two dice out of four in six separate ways to make another pair: dice number 1&2, 1&3, 1&4, 2&3, 2&4 and 3&4,but depending on how you calculate the probability, some of these are included in the others: for example if dice 1&3 show the same number and you have two pair, then dice 2&4 must be pair also. So there can be risk of counting same case twice.

So if you try to do those, post your solutions or ask for help.

 

[Mad Man]

I woke up in a tub of ice with my kidney missing, should I go to the hospital (I don't have insurance) or should i just walk it off?

 

[Brighteye]

walking is a good idea. It will warm you up and return circulation to your extremities. I suggest that you see the mortuary manager on your way out to let him know he's doing a splendid job.
Little niceties really help with getting people on your side.

 

[Huayna Capac357]

No you didn't...

EDIT: Crosspost

 

[Abaddon]

Will you join the game I am running on this forum?

If not, why not?

 

[GoodGame]

I woke up in a tub of ice with my kidney missing, should I go to the hospital (I don't have insurance) or should i just walk it off?

Let us know if you're urinating blood.

 

[Mad Man]

walking is a good idea. It will warm you up and return circulation to your extremities. I suggest that you see the mortuary manager on your way out to let him know he's doing a splendid job.
Little niceties really help with getting people on your side.

Thank you I will as soon as I find a stray cat to swap orgins with.

Will you join the game I am running on this forum?

If not, why not?

what game do you have in mind

 

[Mad Man]

Let us know if you're urinating blood.

I do that any ways. In fact i'm doing it right now!

 

[Abaddon]

Read and click my signature for more info.

 

[GoodGame]

I do that any ways. In fact i'm doing it right now!

Then go see a medical Doctor, quick

 

[Dachs]

Someone please explain to me the logic behind the Macedonian side of the FYROM/Greek naming dispute.

 

[Globex]

What is the quickest and easiest way to solve this problem:

The points (1,2) (6,-2) and (3,7) correspond to the vertices of the triangle ABC. Which set of ordered pairs represent the vertices of a triangle congruent to triangle ABC?

a. (5,5) (8,0) (3,4)
b. (5,7) (4,0) (-4,0)
c. (5,5) (8, -4) (3,0)
d. (3,6) (6, -3) (2,0)
e. (3,5) (4,6) (2,3)

 

[Camikaze]

What is the quickest and easiest way to solve this problem:

The points (1,2) (6,-2) and (3,7) correspond to the vertices of the triangle ABC. Which set of ordered pairs represent the vertices of a triangle congruent to triangle ABC?

a. (5,5) (8,0) (3,4)
b. (5,7) (4,0) (-4,0)
c. (5,5) (8, -4) (3,0)
d. (3,6) (6, -3) (2,0)
e. (3,5) (4,6) (2,3)

Process of elimination. Graph them all and see which one looks like ABC. (a) is too small, as is (e), (b) is way too big, and (d) is too thin. This only leaves c, which is the exact same shape as ABC, shifted two to the right and two down.

Then, if you really want to prove that c is congruent, either measure all the corresponding sides to show congruency (SSS), or do SAS or AAS. These two methods would probably take just as long as SSS.

 

[eastsidebagel]

How can I put multiple quotes in my posts?

 

[Dachs]

How can I put multiple quotes in my posts?

The multiquote button, which is next to the quote button. Just click on the multiquote button for all of the posts you want to quote, then click on the quote button on any one of them for smegtastic epic quoteness.

Nobody likes my question?