Question

Two dice are thrown at the same time. Determine the probability that the sum of the numbers on the two dice is 5.

Hint:

For a sum \( S \) in two dice, the number of favorable outcomes is \( (S-1) \) if \( S \leq 7 \), and \( (13-S) \) if \( S>7 \). Here \( 5-1 = 4 \).

Answer 1

Step 1: Understanding the Concept:
When two dice are thrown, each die has 6 possible outcomes.
The total number of possible outcomes for the pair is the product of individual outcomes.
Step 2: Key Formula or Approach:
Total outcomes \( (n(S)) = 6 \times 6 = 36 \).
Probability of an event \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
Step 3: Detailed Explanation:
Let \( E \) be the event that the sum of the numbers on the two dice is 5.
The possible pairs \( (x, y) \) such that \( x + y = 5 \) are:
1. \( (1, 4) \)
2. \( (2, 3) \)
3. \( (3, 2) \)
4. \( (4, 1) \)
The number of favorable outcomes \( n(E) = 4 \).
Applying the probability formula:
\[ P(E) = \frac{4}{36} \]
Simplifying the fraction:
\[ P(E) = \frac{1}{9} \]
Step 4: Final Answer:
The probability that the sum is 5 is \( \frac{1}{9} \).