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# i don't know where to start.

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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
+101424
+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

Nov 25, 2018
#2
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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
+87
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I had my robot check if this is one of the BB brothers.  It said, “Danger! Will Robinson!”

JacobBernoulli  Nov 26, 2018