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.