To determine the probability of obtaining a sum of at most 4 on a throw of two dice:

Step 1: Total possible outcomes

Each die has 6 faces, so the total number of outcomes when throwing two dice is: $6 \times 6 = 36$

Step 2: Favorable outcomes (sum ≤ 4)

The pairs of dice rolls that give a sum of at most 4 are:

• Sum = 2: (1, 1)
• Sum = 3: (1, 2), (2, 1)
• Sum = 4: (1, 3), (2, 2), (3, 1)

This gives a total of: $1 + 2 + 3 = 6 \text{ favorable outcomes.}$

Step 3: Calculate the probability

The probability of obtaining a sum of at most 4 is: $P(\text{sum ≤ 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{36} = \frac{1}{6}.$

Final Answer:

The probability of obtaining a sum of at most 4 is: $\boxed{\frac{1}{6}}$

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Related Questions:

1. What is the probability of obtaining a sum of exactly 7 when rolling two dice?
2. How many outcomes result in a sum greater than 8 when rolling two dice?
3. What is the probability of rolling doubles on two dice?
4. How many outcomes result in a sum of exactly 10 when rolling two dice?
5. What is the probability of obtaining a sum less than 6 on two dice?

Tip:

When solving probability problems, always consider breaking the problem into favorable outcomes and total possible outcomes for clarity.