Question

What is the probability of getting a sum of \(9\) when two fair dice are rolled simultaneously?

• A. \( \frac{1}{12} \)
• B. \( \frac{1}{9} \)
• C. \( \frac{1}{8} \)
• D. \( \frac{1}{6} \)

Hint:

When two dice are rolled, the total possible outcomes are always \(36\). To find probability, count the number of favorable pairs that produce the required sum.

Answer 1

The Correct Option is B

Concept: When two fair dice are rolled, each die has \(6\) possible outcomes. Therefore, the total number of possible outcomes is: \[ 6 \times 6 = 36 \] Each outcome is equally likely.
Step 1: List all outcomes whose sum is \(9\).
The pairs of numbers whose sum equals \(9\) are: \[ (3,6), (4,5), (5,4), (6,3) \] Thus, the number of favorable outcomes is: \[ 4 \]
Step 2: Apply the probability formula.
The probability of an event is given by: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] Substituting the values: \[ P(\text{sum } = 9) = \frac{4}{36} \]
Step 3: Simplify the fraction.
\[ \frac{4}{36} = \frac{1}{9} \]
Step 4: Conclusion.
Therefore, the probability of obtaining a sum of \(9\) when two fair dice are rolled is: \[ \frac{1}{9} \]