Question

Two fair dice are thrown simultaneously. What is the probability of getting a sum of exactly 9?

• A. \(1/9\)
• B. \(1/12\)
• C. \(1/6\)
• D. \(1/4\)

Hint:

To quickly count sums for two dice, remember the pattern: the number of ways to roll a sum \(S\) (for \(S\) from 2 to 7) is \(S - 1\). For \(S\) from 8 to 12, it is \(13 - S\). For a sum of 9, the ways are \(13 - 9 = 4\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the probability of obtaining a sum of 9 when two six-sided dice are rolled together.


Step 2: Key Formula or Approach:
The probability of an event \(E\) is given by:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

Step 3: Detailed Explanation:
When two fair dice are thrown, each die has 6 faces.
The total number of possible outcomes in the sample space is:
\[ 6 \times 6 = 36 \] Let \(E\) be the event of getting a sum of exactly 9.
We need to find all pairs \((x, y)\) such that \(x + y = 9\), where \(1 \leq x, y \leq 6\).
The favorable outcomes are:
\((3, 6), (4, 5), (5, 4), (6, 3)\)
Thus, the number of favorable outcomes is 4.
Now, substituting these into the probability formula:
\[ P(E) = \frac{4}{36} \] Simplifying the fraction by dividing the numerator and denominator by 4, we get:
\[ P(E) = \frac{1}{9} \]

Step 4: Final Answer:
The correct choice is (A).