+127 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?)
+129852 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
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
+112 I had my robot check if this is one of the BB brothers. It said, “Danger! Will Robinson!”
