* A six-sided die is rolled 2 times. What is the fractional probability of rolling different numbers?

Answer 1

To calculate the probability of rolling different numbers on a six-sided die rolled 2 times, we first need to determine the total number of possible outcomes.

For each roll, there are 6 possible outcomes (numbers 1 through 6). Since we are rolling the die 2 times, the total number of possible outcomes is calculated by multiplying the number of outcomes for each roll: 6 x 6 = 36.

Next, we need to determine the number of favorable outcomes, which in this case is when we roll different numbers on each of the 2 rolls. To calculate this, we need to consider the total number of ways to choose different numbers for each roll.

For the first roll, there are 6 options. For the second roll, there are 5 remaining options (since we cannot repeat the number from the first roll). Therefore, the total number of favorable outcomes is: 6 x 5 = 30.

Finally, we can calculate the fractional probability of rolling different numbers as the ratio of favorable outcomes to total outcomes:

30 / 36 = 5 / 6

So, the fractional probability of rolling different numbers on a six-sided die rolled 2 times is 5/6.