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:
We are asked to find the probability of rolling a total sum of 9 using two standard six-sided dice.


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

Step 3: Detailed Explanation:
Rolling two dice yields a total sample space of:
\[ 6 \times 6 = 36 \text{ possible outcomes} \] Let \(E\) represent the event where the sum of the two dice is exactly 9.
We list all possible pairs \((x, y)\) that satisfy \(x + y = 9\):
\((3, 6), (4, 5), (5, 4), \text{ and } (6, 3)\)
This gives us exactly 4 favorable outcomes.
Plugging these values into our probability formula gives:
\[ P(E) = \frac{4}{36} \] Reducing the fraction by dividing both the numerator and denominator by 4 results in:
\[ P(E) = \frac{1}{9} \]

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