This is an example of an INDEPENDENT event:
The probability of throwing a double six with two dice is the result of throwing six with the first die and six with the second die. The total possibilities are, one from six outcomes for the first event and one from six outcomes for the second, Therefore (1/6) * (1/6) = 1/36th or 2.77%.
The two events are independent, since whatever happens to the first die cannot affect the throw of the second, the probabilities are therefore multiplied, and remain 1/36th.
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If they are normal dice, the probability is 0.
Throwing two dice, there are a total of 36 combinations (1-1, 1-2, 1-3, etc.), each of which has the same probability. Of these, the following give a sum of nine: 3-6, 4-5, 5-4, 6-3. That makes four favorable cases, or a probability of 4/36.
The probability of rolling a 4 in a die is 1 in 6, or about 0.1667. The probability, then, of rolling a 4 in at least one of two dice rolls is twice that, or 2 in 6, or 0.3333. The probability of rolling a sum of 4 in two dice is 3 in 36, or 1 in 18, or about 0.05556.
The probability of rolling a 7 with 2 dice is 6/36; probability of rolling an 11 is 2/36. Add the two together to find probability of rolling a 7 or 11 which is 8/36 or 2/9.
There are 36 permutations of two dice. Of these, 9 have a sum of 5 or 6, so the probability of rolling a sum of 5 or 6 on two dice is 9 in 36, or 1 in 9, or about 0.1111.