If 2 fair dice are rolled together , what is the probability that the sum will be 9

1)Is the probability 4/36 (1/9); as no. of favorable cases are {(3,6);(6,3);(4,5);(5,4)} ?

2) Or is it 2/36 (1/18); as no. of favorable cases are {(3,6);(4,5)} the reason I am confused is that the question does not state if the dices are distinguishable or not. If they are not distinguishable then the answer should be 1/18 as stated in case 2. Is my understanding correct?

  • $\begingroup$ Hint: in scenario 2, are there really 36 different cases in total? $\endgroup$ – Moyli Nov 29 '15 at 15:44
  • $\begingroup$ Even if the dice are NOT distinguishable, the probability of $(4,5)$ is $\frac{2}{36}$. $\endgroup$ – barak manos Nov 29 '15 at 15:48

If the dice are not distinguishable then the total number of outcomes is only 21 (15 where they are different and 6 where they are equal) and even those 21 do not all have equal probability (the 6 have each only half the likelihood of the 15). So by a detour we also arrive at 1/9 if they are indistinguishable.


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