suppose you roll 2 number cubes. what is the probability that the product of the numbers is a multiple of 7
To determine the probability of rolling two number cubes and getting a product that is a multiple of 7, we need to find the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the total number of outcomes:
Since each number cube has 6 faces numbered 1 to 6, the total number of outcomes for rolling two cubes is 6 * 6 = 36.
Next, let's find the number of favorable outcomes:
To have a product that is a multiple of 7, we need to consider the combinations of numbers on the two cubes that could yield such products.
The factors of 7 are 1 and 7, so we need to find the combinations that contain at least one of these factors.
1. When one cube shows a 1, we need the other cube to show a 7. There is only 1 possible combination for this scenario: (1, 7) or (7, 1).
2. When one cube shows a 7, we have the same scenario as above. Again, there is only 1 possible combination: (7, 1) or (1, 7).
Therefore, the total number of favorable outcomes is 2.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes)/(Total number of possible outcomes)
= 2/36
= 1/18
So, the probability of rolling two number cubes and getting a product that is a multiple of 7 is 1/18.