Final answer:
To find the probability of getting a product of 6 when two dice are rolled, you need to determine the number of favorable outcomes and the total number of possible outcomes. There are 4 favorable outcomes out of 36 total outcomes, so the probability is 1/9.
Step-by-step explanation:
To find the probability that the product of the two numbers on the top of two different dice is 6, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The question involves calculating the probability that the product of the numbers that come up after tossing two different dice is 6. To find this probability, we need to look at the possible combinations of dice rolls that yield a product of 6.
These combinations are (1,6), (2,3), (3,2), and (6,1). Since each die is six-sided, there are a total of 6 × 6 = 36 possible outcomes when two dice are rolled. Out of these, only four outcomes give us a product of 6. Therefore, the probability of the product being 6 is 4/36, which simplifies to 1/9.
We use the sample space, which includes 36 outcomes for two dice, and count the favorable outcomes that result in the product of 6. The product rule is not directly applied here as we are not looking for a combination of independent probabilities, but the total number of favorable outcomes is a direct count.
- There are 6 possible outcomes for each die, ranging from 1 to 6.
- To find the favorable outcomes, we need to determine the number of different combinations of two numbers whose product is 6.
- These combinations are (1, 6), (6, 1), (2, 3), and (3, 2), so there are 4 favorable outcomes.
- The total number of possible outcomes is 6 x 6 = 36.
- Therefore, the probability of obtaining a product of 6 is 4/36, which simplifies to 1/9.