We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
150
3
avatar+128 

I have 4 6-sided dices, number 1-6, and I roll them all. What is the probablity that the sum of the first two equals the sum of the last two?

 

 

(I know the denominator is 6^4... but how do you find the numerator?)

 Nov 25, 2018
 #1
avatar+99415 
+1

Here's my best attempt, ME....

 

Probability  of rollling

 

2 on first pair and 2 on second pair   =   (1/36) * (1/36) = (1/36)^2

3 on first pair and 3 on second pair  =  (2/36) * (2/36) = (2/36)^2

4 on first pair and 4 on second pair = (3/36) * (3/36) = (3/36)^2

5  and 5      =    (4/36) * (4/36)    =   (4/36)^2

6 and 6      =     (5/ 36) * ( 5/36)   = (5/35)^2

7 and 7       =    (6/36) * (6/36)

8 and 8  = (5/36)^2

9 and 9  = (4/36)^2

10 and 10 = (3/36)^2

11 and 11 = (2/36)^2

12 and 12 = (1/36)^2

 

So.....the probability is

 

( 2 [ 1^2 + 2^2 + 3^2 + 4^2 + 5^2] + 6^2 )  /  6^4     =   

 

146 / 1296  = 

 

73 / 648

 

 

cool cool cool

 Nov 25, 2018
 #2
avatar
0

1+1+1+1 = 4...................1 permutations
2+2+1+1 = 6...................6
3+3+1+1 = 8...................6
3+2+2+1 = 8..................12
2+2+2+2 = 8..................1

4+4+1+1 = 10................6 
4+3+2+1 = 10................24
3+3+2+2 = 10.................6       
5+5+1+1 = 12.................6                                                 
5+4+2+1 = 12................24
5+3+3+1 = 12................12
4+4+2+2 = 12.................6
4+3+3+2 = 12................12
3+3+3+3 = 12............... 1  

6+6+1+1 = 14................6
6+5+2+1 = 14................24
6+4+3+1 = 14................24
5+5+2+2 = 14................6
5+4+3+2 = 14................24
4+4+3+3 = 14.................6

6+6+2+2 = 16.................6
6+5+3+2 = 16................24
6+4+4+2 = 16................12
5+5+3+3 = 16.................6
5+4+4+3 = 16.................12
4+4+4+4 = 16................ 1

6+6+3+3 = 18................6
6+5+4+3 = 18...............24
5+5+4+4 = 18................6

6+6+4+4 = 20................6
6+5+5+4 = 20................12
5+5+5+5 = 20............... 1

6+6+5+5 = 22................6

6+6+6+6 = 24................1 

Note: I had the computer list them all. Somebody should check this. I get a total of:

336 / 6^4 =7 / 27                                                 

 Nov 26, 2018
 #3
avatar+86 
0

I had my robot check if this is one of the BB brothers.  It said, “Danger! Will Robinson!”

JacobBernoulli  Nov 26, 2018

15 Online Users

avatar
avatar
avatar