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

Step 1: Understanding the Concept:
The difference refers to the absolute value of the difference between the two numbers shown on the dice.
Step 2: Detailed Explanation:
Total possible outcomes \( n(S) = 36 \).
Let \( F \) be the event that the difference is 3. We list the pairs \( (x, y) \) such that \( |x - y| = 3 \):
1. \( (1, 4) \) and \( (4, 1) \)
2. \( (2, 5) \) and \( (5, 2) \)
3. \( (3, 6) \) and \( (6, 3) \)
Counting these pairs, the number of favorable outcomes \( n(F) = 6 \).
Calculating the probability:
\[ P(F) = \frac{6}{36} \]
Simplifying the fraction:
\[ P(F) = \frac{1}{6} \]
Step 3: Final Answer:
The probability that the difference is 3 is \( \frac{1}{6} \).