Two standard number cubes are rolled. Find each probability.
12. P(a sum equal to 12)
13. P(sum not equal to 2)
14. P(a product equal to 15)
15. P(a product not equal to 15)
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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