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do you agree with here,

Clayface
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Ovi
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other
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Total Members Voted: 9

Author Topic: 1 rigged dice and 1 normal  (Read 3276 times)

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Offline Clayface

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1 rigged dice and 1 normal
« on: October 19, 2006, 05:41:13 pm »
Ok, well me and ovi have been having a discussion about dice,
if you have 1 loaded dice, with a 1/4 chance of getting a 1 and a 1/4 chance of getting a 6
and a normal die with 1/6 chance of getting everything
what is the chance of getting a 7 when rolling 1 loaded die and 1 normal die?



and here is my math

1/2 chance of it laninding on 1 or 6 on the loaded die, right
1/2 * 1/6 = 1/12
that is the chance of it landing on 1 or 6 on the loaded die, or any number on the other die
how many ways can you make seven out of that,
2 ways
so, you can get 6 and 1, or 1 and 6, so thats 2 ways
so that is 2/12 or 1/6
1/6th chance to get 7 with it landing on either the 1 or 6 on the loaded die

then the rest of that die
you have a 1/2 chance to get 2-5 on the loaded die
1/2 * 1/6 = 1/12
as in a 1/12 chance of it not landing on one of the rigged numbers and any other number on the other die
1/12 chance of it being a 2 2 , 2 3, 2 4 etc etc
how many ways can you make seven,
4 ways
so thats 4/12'ths
4/12'ths chance of getting a 7 without it landing on 1 or 6 on the loaded die
so that is 4/12ths, or 1/3

so you have a 1/6ths chance of it being a 7 with it being 1 or 6 on the rigged die
or a 1/3 chacne of it being a 7 without getting a 1 or a 6 on the rigged die
so you have a 1/2rd chance of getting a 7 if you roll 1 rigged die and 1 normal die

« Last Edit: October 19, 2006, 05:57:13 pm by Clayface »



Offline Oviraptor

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Re: 1 rigged dice and 1 normal
« Reply #1 on: October 19, 2006, 05:43:30 pm »


Therefore making it 1/6 of a chance to roll a seven.

Please ask if you think it needs explaining.

Offline stuck

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Re: 1 rigged dice and 1 normal
« Reply #2 on: October 19, 2006, 05:45:19 pm »
Lol, that's great ovi.

Quote
1/2 chance of it laninding on 1 or 6 on 1 die, right

Err, isn't their a 2/6 chance or 1/3 chance? (unless this die is different, somehow)

EDIT: Oh, now its loaded. Makes more sense.
« Last Edit: October 19, 2006, 05:58:51 pm by stuckin2004 »

Offline Vivec

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Re: 1 rigged dice and 1 normal
« Reply #3 on: October 19, 2006, 05:53:23 pm »
Hahaha, clayface, you didn't have to do this.
Vivec, you're the best forum member ever.

Offline Clayface

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Re: 1 rigged dice and 1 normal
« Reply #4 on: October 19, 2006, 05:54:41 pm »
ohh I did though

Offline Oviraptor

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Re: 1 rigged dice and 1 normal
« Reply #5 on: October 19, 2006, 05:58:44 pm »
The actual question was: "A six-sided trick die comes up '6' one-fourth of the time and '1' one-fourth of the time. The other faces come up one-eigth of the time. What is the probability of rolling a sum of 7 using this trick die and a fair die?"

Might want to change it to that.

Offline syphonbyte

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Re: 1 rigged dice and 1 normal
« Reply #6 on: October 19, 2006, 08:21:14 pm »
Yes, otherwise it is terribly confusing.

Honestly I'm too lazy to do the math for this so if I'm bored later I'll probably just find an expected outcome by running a simulation a few thousand times. That's a lot more fun anyhow.

Offline GrapeFruit

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Re: 1 rigged dice and 1 normal
« Reply #7 on: October 20, 2006, 10:30:48 am »
Here's how it works much easier:
Possible combinations resulting in a sum of 7:  1L (means loaded dice shows 1) and 6N (normal dice shows 6)
  1L, 6N   1/4*1/6=1/24
  2L, 5N   1/8*1/6=1/48    (1/8 because 2L's chance is at 1/4 of 1/2)
  3L, 4N   1/8*1/6=1/48
  4L, 3N   1/8*1/6=1/48
  5L, 2N   1/8*1/6=1/48
  6L, 1N   1/4*1/6=1/24

All added up results in: 1/6

A chance of 16.67% a sum of 7

So Oviraptor is right, although his way to the result seems a bit confusing at the first glance.

Edit: Ok, now I see, we actually did the same
« Last Edit: October 20, 2006, 10:41:43 am by GrapeFruit »
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Offline Genesis

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Re: 1 rigged dice and 1 normal
« Reply #8 on: October 20, 2006, 10:41:31 am »
Yes, I have to agree with Oviraptor on this. I have found a much, much simpler explination though.

Rigged dice lands on a number. (It makes no diffrence how it was rigged or for what results.)

The normal dice has a 1/6 chance of landing on the corresponding number to make it 7.

That should be an easier explanation to understand.

What will you do?