https://file.aiquickdraw.com/mathbot/file/1728879685094m132tqs4.jpg

The text in the image is in Indonesian and translates to the following:

"3. Two dice are thrown simultaneously. Determine the probability of:
(4) The sum of the dice equals 7
(5) The difference of the dice equals 3"

Let's solve these:

### (4) Probability that the sum equals 7:
When two six-sided dice (with faces numbered 1 to 6) are rolled, the possible sums range from 2 to 12. The total number of outcomes when rolling two dice is \(6 \times 6 = 36\).

The pairs that give a sum of 7 are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)

There are 6 outcomes that give a sum of 7. Hence, the probability is:
\[
P(\text{sum} = 7) = \frac{6}{36} = \frac{1}{6}
\]

### (5) Probability that the difference equals 3:
The difference between two dice results can be 3 in the following cases:
- (1, 4)
- (2, 5)
- (3, 6)
- (4, 1)
- (5, 2)
- (6, 3)

There are also 6 outcomes that result in a difference of 3. Thus, the probability is:
\[
P(\text{difference} = 3) = \frac{6}{36} = \frac{1}{6}
\]

Would you like a more detailed explanation or have any additional questions?

### Related Questions:
1. What is the probability of getting a sum of 8 when rolling two dice?
2. How do you calculate the probability of rolling doubles (same number on both dice)?
3. What is the probability of getting a sum less than 5 with two dice?
4. If three dice are rolled, what is the probability that the sum equals 10?
5. How do the probabilities change if a die is biased (loaded)?

### Tip:
When calculating probabilities with dice, always remember to count all possible outcomes, which for two fair six-sided dice is 36. This helps in determining the probability accurately.

Determine the probability when two dice are rolled: (4) The sum of the dice equals 7. (5) The difference of the dice equals 3.

Calculate the probability of rolling a sum of 7 or a difference of 3 when two dice are thrown. Learn about basic probability concepts and combinatorics with step-by-step explanations. Suitable for students in Grades 6-8.

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