Two dice numbered 1 to 6 are thrown together and scores are added. The probability that the sum will be 4 is:

To find the probability that the sum of two dice will be 4, we start by considering all the possible outcomes when two dice are thrown. Each die has 6 faces, so there are a total of \( 6 \times 6 = 36 \) possible outcomes.

Next, we determine the number of favorable outcomes that result in a sum of 4. We list these outcomes:

1. Die 1: 1, Die 2: 3 → Sum = 1 + 3 = 4
2. Die 1: 2, Die 2: 2 → Sum = 2 + 2 = 4
3. Die 1: 3, Die 2: 1 → Sum = 3 + 1 = 4

There are 3 favorable outcomes.

The probability \( P \) of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Thus,

\[
P(\text{sum of 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{36} = \frac{1}{12}
\]

So, the probability that the sum of the numbers on the two dice will be 4 is \( \frac{1}{12} \).

Would you like further details or have any questions about this solution?

Here are 8 relative questions that expand on this topic:

1. What is the probability of rolling a sum of 7 with two dice?
2. How many outcomes are there when rolling three dice?
3. What is the probability of rolling a sum of 11 with two dice?
4. How do you calculate the probability of rolling doubles with two dice?
5. What is the probability of getting a sum greater than 8 with two dice?
6. If one die is rolled, what is the probability of getting an even number?
7. How does the probability change if the dice are not fair?
8. Can you list all the sums that can be achieved with two dice and their respective probabilities?

**Tip:** When calculating probabilities for dice, it's often helpful to list all possible outcomes to ensure you count all favorable outcomes correctly.

Discover the probability of rolling a sum of 4 with two dice. Learn the step-by-step calculation and understand the concept of probability in dice throws. Suitable for students in Grades 6-8.

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