Question

sample response: a table can show all the possible sums for two number cubes. using the table, there are 6 ways to get 7, and 36 possible sums, so the probability is 6/36 = 1/6. check all that you considered in your response. make a table or list to show the possible outcomes. the outcomes that have a sum of 7 are 1 and 6, 6 and 1, 2 and 5, 5 and 2, 3 and 4, and 4 and 3. to find the probability, divide the number of desired outcomes by the number of possible outcomes.

Explanation:

Step1: Identify method for outcomes

Making a table or list shows all possible outcomes when rolling two number - cubes.

Step2: List favorable outcomes

The pairs that sum to 7 are (1,6), (6,1), (2,5), (5,2), (3,4), (4,3), so there are 6 favorable outcomes.

Step3: Calculate total outcomes

Each number - cube has 6 faces. When rolling two number - cubes, the total number of possible outcomes is \(6\times6 = 36\) according to the multiplication principle.

Step4: Calculate probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of desired outcomes}}{\text{Number of possible outcomes}}\). So \(P=\frac{6}{36}=\frac{1}{6}\).

Answer:

All of the above should be considered. That is, making a table or list to show the possible outcomes, identifying the outcomes that have a sum of 7, and using the formula to find the probability by dividing the number of desired outcomes by the number of possible outcomes.