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

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

We need: The sum of the numbers on the two dice = 5

Step 1: List all favourable outcomes
The pairs whose sum is 5 are:
• (1, 4)
• (2, 3)
• (3, 2)
• (4, 1)

Number of favourable outcomes = 4

Step 2: Compute probability
\[ P(\text{sum = 5}) = \frac{4}{36} = \frac{1}{9} \]

Final Answer:
\[ \boxed{\frac{1}{9}} \]