Write $0.\overline{12}$ as a fraction.
Answer (2)
Explains the probabilities for each scenario when rolling two standard number cubes.
For the given questions:
P(a sum equal to 12): This can happen only with the combination of 6 and 6 when both dice show 6. So, the probability is 1/36.
P(sum not equal to 2): The sum will not be 2 when either one or both dice show numbers other than 1. Thus, the probability is 35/36.
P(a product equal to 15): The product will be 15 only with the combination of 5 and 3 or 3 and 5, giving a probability of 2/36.
P(a product not equal to 15): The product will not be 15 in all other cases, resulting in a probability of 34/36.
In summary, the probabilities are: P(a sum equal to 12) = 1/36, P(sum not equal to 2) = 35/36, P(a product equal to 15) = 1/18, and P(a product not equal to 15) = 17/18.
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