Can any math whizzes tell me the odds of the following after rolling five dice one time?
-All odd numbers
-All even numbers
-Total sum less than 10
-Total sum greater than 25.
Thanks!
help with probabilities (rolling 5 dice)
Thu, 02/07/2013 - 14:37
Thu, 02/07/2013 - 14:46
#1
Assuming all 6-sided
Assuming all 6-sided dice:
All Odd = 3.125% chance (0.5^5)
All Even = Same as above
Sum < 10 = 0.2058% chance (1/3)^4 * (1/6)
Sum > 25 = Same as above
Hope this helps.
Thu, 02/07/2013 - 19:39
#3
I think your % for <10 and
[edit: re-read your numbers, re-checked my maths, re-posted!]
I think your 0.2% for <10 and >25 look on the low side..
I'm not the greatest at maths so I found these diagrams of the standard distribution using 5d6 on some math guys blogs:
http://photos1.blogger.com/blogger/6863/540/1600/dice5.png
http://dinodini.files.wordpress.com/2011/03/msp86419f157hhi439i1c100002b...
It's not all that clear, but the chances of rolling 10 are 0.02 (2%) and 9 is about 0.01 (1%) and then 8 is 0.005 (0.5%).. adding all these up, I'd estimate your chances are ~3.5%.
This would of course, be the same for >25.
I'm mediocre at Maths and so await being corrected! ;-)
HTH
Fri, 02/08/2013 - 06:03
#4
TwentyPercent wrote:Sum < 10
Sum < 10 = 0.2058% chance (1/3)^4 * (1/6)
Sum > 25 = Same as above
Sum > 25 = Same as above
As far as I can see, that would be the chance of rolling no higher than a two on the first four dice, plus the final die must be exactly 1.
However, it is also possible to roll less than ten with other permutations, such as 33111 or 21222, so the actual chance should be higher.
Fri, 02/08/2013 - 08:37
#5
Dulkal wrote:TwentyPercent
Sum < 10 = 0.2058% chance (1/3)^4 * (1/6)
Sum > 25 = Same as above
Sum > 25 = Same as above
As far as I can see, that would be the chance of rolling no higher than a two on the first four dice, plus the final die must be exactly 1.
However, it is also possible to roll less than ten with other permutations, such as 33111 or 21222, so the actual chance should be higher.
You are correct; I was only looking at a single scenario. Below are the all the scenarios I see that would give Sum<10. This chance definitely seems lower than that probability chart, but I'd like to know why below wouldn't be correct.
Dice1 1 1 1 1 1
Dice2 1 1 1 2 1
Dice3 1 1 2 2 1
Dice4 1 2 2 2 3
Dice5 5 4 3 2 3
Scenario % 0.00429% 0.10288% 0.15432% 0.20576% 0.11574%
Total % 0.58299%
Fri, 02/08/2013 - 10:49
#7
But there are five
But there are five permutations for:
4 x 1 and 1 x 2, i.e. 11112 11121 11211 12111 21111 (Dice 2 above)
There are ten for Dice 3:
11122 11212 11221 12112 12121 12211 21112 21121 21211 22111
There's another 5 each for 11113, 11114, 11115, 11116.
Plus permutations for 11123, 11133, 11134...
Have to stop now, my head is spinning :)
Fri, 02/08/2013 - 18:44
#10
Dice Probabilities
This seems like a good thread to post this on.
Fri, 02/08/2013 - 19:30
#11
This is a script for nanDECK
This is a script for nanDECK for calculating permutations:
PR[dice]5=1|2|3|4|5|6
[less10]=FILTER(+[dice],5,6,7,8,9)
[more25]=FILTER(+[dice],26,27,28,29,30)
FONT=Arial,16,,#000000
TEXT=1,"Total={(dice)}",0,0,100%,10%
TEXT=1,"Less than 10={(less10)}",0,10%,100%,10%
TEXT=1,"More than 25={(more25)}",0,20%,100%,10%
The result is:
Total=7776
Less than 10=126
More than 25=126
And nanDECK can print (or save into a file) all the sequences of results. For example, these are the 126 rolls < 10:
11111
11112
11113
11114
11115
11121
11122
11123
11124
11131
11132
11133
11141
11142
11151
11211
11212
11213
11214
11221
11222
11223
11231
11232
11241
11311
11312
11313
11321
11322
11331
11411
11412
11421
11511
12111
12112
12113
12114
12121
12122
12123
12131
12132
12141
12211
12212
12213
12221
12222
12231
12311
12312
12321
12411
13111
13112
13113
13121
13122
13131
13211
13212
13221
13311
14111
14112
14121
14211
15111
21111
21112
21113
21114
21121
21122
21123
21131
21132
21141
21211
21212
21213
21221
21222
21231
21311
21312
21321
21411
22111
22112
22113
22121
22122
22131
22211
22212
22221
22311
23111
23112
23121
23211
24111
31111
31112
31113
31121
31122
31131
31211
31212
31221
31311
32111
32112
32121
32211
33111
41111
41112
41121
41211
42111
51111
awesome!