Question

The probability of getting a sum of 8, when two dice are thrown simultaneously, is :

• A. $\frac{1}{12}$
• B. $\frac{1}{9}$
• C. $\frac{1}{6}$
• D. $\frac{5}{36}$

Answer 1

The Correct Option is D

Step 1: Understanding the problem:
We are asked to find the probability of getting a sum of 8 when two dice are thrown simultaneously.
The probability of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] We need to find the number of favorable outcomes for a sum of 8 and divide it by the total possible outcomes when two dice are thrown.

Step 2: Total number of possible outcomes:
When two dice are thrown, each die has 6 faces, so the total number of possible outcomes is:
\[ \text{Total outcomes} = 6 \times 6 = 36 \]

Step 3: Finding the favorable outcomes for a sum of 8:
The possible pairs of dice rolls that result in a sum of 8 are:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)
Thus, there are 5 favorable outcomes.

Step 4: Calculating the probability:
Now, we can calculate the probability of getting a sum of 8 by dividing the number of favorable outcomes by the total number of possible outcomes:
\[ P(\text{sum of 8}) = \frac{5}{36} \]

Conclusion:
The probability of getting a sum of 8 when two dice are thrown simultaneously is \( \frac{5}{36} \).