A number cube with sides labeled 1 through 6 is rolled two times, and the sum of the numbers that end face up is calculated. What is the probability that the sum of the numbers is 3?

rolling the same die twice is no different than rolling 2 dice.

to get a three ...
1 2
2 1 ----> two ways
prob(3) = 2/36 = 1/18

Well, you know what they say, when life gives you a number cube, you roll it! So, let's figure out the probability of getting a sum of 3.

To do this, we need to know the possible outcomes. When you roll a number cube twice, you have a total of 36 possible outcomes (6 sides on the first roll multiplied by 6 sides on the second roll).

Now let's see how many of these 36 outcomes result in a sum of 3. There are only two possibilities: rolling a 1 and a 2, or rolling a 2 and a 1. So, we have 2 desired outcomes.

Therefore, the probability of getting a sum of 3 is 2/36, which simplifies to 1/18.

Remember, next time you're feeling bored, just roll the dice and let the numbers decide your fate!

To find the probability of rolling a sum of 3 with two rolls of a number cube, we need to determine the number of favorable outcomes (sum of 3) and the total number of possible outcomes.

Step 1: Determine the total number of possible outcomes.
Since we're rolling a number cube two times, there are 6 possible outcomes for each roll. Therefore, the total number of possible outcomes is 6 × 6 = 36.

Step 2: Determine the number of favorable outcomes.
To obtain a sum of 3, we need the following combinations:
- Roll 1: 1 and Roll 2: 2
- Roll 1: 2 and Roll 2: 1

So, there are 2 favorable outcomes.

Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.

Probability = Favorable outcomes / Total outcomes

Substituting the values we found,
Probability = 2 / 36 = 1 / 18

Therefore, the probability of rolling a sum of 3 is 1/18.

Note: Remember, probabilities are always expressed as fractions, decimals, or percentages.

To find the probability of getting a sum of 3 when rolling a number cube two times, we need to first determine the number of ways we can get a sum of 3 and then divide that by the total number of possible outcomes.

We can obtain a sum of 3 in the following ways:
- Rolling a 1 on the first roll and a 2 on the second roll.
- Rolling a 2 on the first roll and a 1 on the second roll.

These are the only two possibilities, as the sum of the numbers rolled cannot exceed 3 since the maximum value on the number cube is 6.

Now, let's calculate the total number of possible outcomes. Since we are rolling a number cube two times, there are 6 possible outcomes for each roll. Therefore, the total number of possible outcomes is 6 * 6 = 36.

Since we have two favorable outcomes (1 + 2 and 2 + 1) and a total of 36 possible outcomes, we can calculate the probability as:
2 favorable outcomes / 36 total outcomes = 1/18.

Therefore, the probability of getting a sum of 3 when rolling a number cube two times is 1/18.