Question

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 3.

Hint:

Always remember to count both orders \( (x, y) \) and \( (y, x) \) unless the numbers are the same (which isn't possible for a non-zero difference).

Answer 1

When two dice are thrown:
Total possible outcomes = 6 × 6 = 36

We need: The difference of the numbers on the two dice = 3

That means:
\[ |a - b| = 3 \]
Step 1: List all favourable outcomes
• (4, 1) → 4 − 1 = 3
• (5, 2) → 5 − 2 = 3
• (6, 3) → 6 − 3 = 3
• (1, 4) → 4 − 1 = 3
• (2, 5) → 5 − 2 = 3
• (3, 6) → 6 − 3 = 3

Number of favourable outcomes = 6

Step 2: Compute probability
\[ P(\text{difference = 3}) = \frac{6}{36} = \frac{1}{6} \]

Final Answer:
The probability is \[ \boxed{\frac{1}{6}} \]