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re: Help me figure out a dice/math question

Posted on 10/31/16 at 11:53 am to
Posted by LSU_Saints_Hornets
Uptown NO,LA
Member since Jan 2013
9739 posts
Posted on 10/31/16 at 11:53 am to
quote:

Of course rolling more dice adds to the probability that ONE of them will turn up a 1 or a 5. Do you seriously think you could roll 1000 dice and there'd be a 66% chance that NONE of them would come up either 1 or 5?

The probability is the same for each die, but the more dice you roll, the better your chances that ONE of them will be what you need (in this case, 1 or 5).





Yea I should have never ventured into explaining this but I get what you are saying the probability that the probability of rolling a 1 or a 5 will increase when you add more die. I was wrong, but I knew that the odds did not double because he doubled the sample.
Posted by LSUBoo
Knoxville, TN
Member since Mar 2006
104440 posts
Posted on 10/31/16 at 11:54 am to
36 possible combinations of two dice.

16 of them don't contain a 1 or a 5.

20 of them do.

Pretty easy to figure out from there.
Posted by Chucktown_Badger
The banks of the Ashley River
Member since May 2013
37550 posts
Posted on 10/31/16 at 11:57 am to
quote:

This sounds like the kind of problem that would never get figured out after a few beers.


We gave up on it. But I kept rolling when I was down to two dice and it sure as hell didn't feel like I was getting a 1 or 5 55% of the time.
Posted by Chucktown_Badger
The banks of the Ashley River
Member since May 2013
37550 posts
Posted on 10/31/16 at 11:57 am to
quote:

I knew that the odds did not double because he doubled the sample.


As did we.
Posted by bmy
Nashville
Member since Oct 2007
48203 posts
Posted on 10/31/16 at 11:58 am to
33% first toss
33% second toss
33% third toss

Roughly 58% that you will roll a 1 or a 5 over three consecutive tosses
This post was edited on 10/31/16 at 12:00 pm
Posted by LSUBoo
Knoxville, TN
Member since Mar 2006
104440 posts
Posted on 10/31/16 at 12:06 pm to
quote:

We gave up on it. But I kept rolling when I was down to two dice and it sure as hell didn't feel like I was getting a 1 or 5 55% of the time.


Well risk/reward you should probably quit when down to two dice, because there's only a 1/9 chance you're going to roll a 1 or 5 on both dice. So you're risking whatever you have built up for an extra 50 or 100 points... not usually worth it.
Posted by Fred Farkle
Member since Jun 2008
617 posts
Posted on 10/31/16 at 12:06 pm to
2 dice. 12 total faces. 4 "good faces".

Probability of NO 1s or 5s is 2/3rds on each die.

2/3 X 2/3 - .445 = The probability that no ones or fives come up on both die. So subtract that from 1 and you get a prob of .555 that when you roll two dice a one or five will show up on one of the two.
Posted by Chucktown_Badger
The banks of the Ashley River
Member since May 2013
37550 posts
Posted on 10/31/16 at 12:08 pm to
quote:

2 dice. 12 total faces. 4 "good faces".

Probability of NO 1s or 5s is 2/3rds on each die.

2/3 X 2/3 - .445 = The probability that no ones or fives come up on both die. So subtract that from 1 and you get a prob of .555 that when you roll two dice a one or five will show up on one of the two.


Farkle is in your name, of course you'd have the correct answer as well.
Posted by 81Tiger
LSU Alumnus
Member since Sep 2009
6855 posts
Posted on 10/31/16 at 12:14 pm to
For those who need to visualize it, these are the possibilities:


1,1 1,2 1,3 1,4 1,5 1,6

2,1 2,2 2,3 2,4 2,5 2,6

3,1 3,2 3,3 3,4 3,5 3,6

4,1 4,2 4,3 4,4 4,5 4,6

5,1 5,2 5,3 5,4 5,5 5,6

6,1
6,2 6,3 6,4 6,5 6,6


20 of the 36 possible outcomes contain a 1 or a 5.

20/36 = 55.5%
Posted by castorinho
13623 posts
Member since Nov 2010
88325 posts
Posted on 10/31/16 at 12:24 pm to
The easiest way to do a this is to determine the odds of rolling neither on each dice then subtracting that number from 1. If you always remember that, then you don't need to memorize a formula

So 1-4/6*4/6
Posted by castorinho
13623 posts
Member since Nov 2010
88325 posts
Posted on 10/31/16 at 12:25 pm to
quote:

I'm pretty sure it's still 1/3.

4 chances of 12 to get one of those numbers.

six upvotes
Posted by TigerstuckinMS
Member since Nov 2005
33687 posts
Posted on 10/31/16 at 1:30 pm to
288

OT, I am disappoint.
Posted by CajunPhil
Chimes
Member since Aug 2013
828 posts
Posted on 10/31/16 at 5:29 pm to
Prob of (1 or 5 on 1st die ) plus prob ( 1 or 5 on 2nd ) - prob of (1 or 5 on both dir ) equals
2/6 plus 2/6 minus 4/36 equals 20/36.

Castorinfo also correct. 1 minus prob of no 1s or 5s on two tosses equals 1 - 16/36

Equals. 20/36.

Fair betting odds on at least one 1 or 5 on two rolls is 1 to 1.2. i.e. Bet 12 to win 10.
This post was edited on 10/31/16 at 5:38 pm
Posted by gthog61
Irving, TX
Member since Nov 2009
71001 posts
Posted on 10/31/16 at 6:33 pm to
That is about as clear as it gets.
Posted by Pectus
Internet
Member since Apr 2010
67302 posts
Posted on 10/31/16 at 6:42 pm to
I love farkle.

It is 33% chance to roll a 1 or 5 on one die.


In fact is it 200% chance you will hit 1 or 5 on roll 1!!
This post was edited on 10/31/16 at 6:44 pm
Posted by Pectus
Internet
Member since Apr 2010
67302 posts
Posted on 10/31/16 at 6:43 pm to
As a rule, I don't roll on 2 left.

I do roll on triple 2s.

Posted by foshizzle
Washington DC metro
Member since Mar 2008
40599 posts
Posted on 10/31/16 at 7:01 pm to
quote:

To get the odds that it will happen, you have to calculate the odds that it won't happen, and subtract that from 100%.

2/3 x 2/3 = 4/9 chance that you won't roll a 1 or 5 on either, or a 5/9 chance that you will.



This right here.

quote:


Unless, of course, you are me playing backgammon and need a 1 or a 5 to get out of jail, in which case the probability of rolling a 1 or a 5 is precisely zero.



And also this.
Posted by CajunPhil
Chimes
Member since Aug 2013
828 posts
Posted on 10/31/16 at 7:19 pm to
Yes, 5/9 = 20/36
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