Unlucky 13 in the dice
Mr. A has 3 fair dice: one of them has 8 faces, numbered 1 to 8. the other has 12 faces numbered 1 to 12 and the other has 20 faces numbered 1 to 20. What is the probability that when they are all thrown together, a sum which is a multiple of 13 shows up?
The answer is 0.0769.
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1 solution
Moderator note:
Can you solve this without computer assistance? How?
I wrote a simple code in MATLAB and got the solution. It will be great to see an analytical solution !!!
nTrials = 1e5; npass=0; for i=1:nTrials dice1 = floor(randi([1,8])); dice2 = floor(randi([1,12])); dice3 = floor(randi([1,20])); sum = dice1+dice2+dice3; if(rem(sum,13)==0) npass=npass+1; end end prob=npass/nTrials;