Question

Find the probability of getting the sum as a perfect square number when two dice are thrown together.

• A. \( \frac{5}{12} \)
• B. \( \frac{7}{18} \)
• C. \( \frac{7}{36} \)
• D. None of these

Hint:

When calculating probabilities for dice sums, list all possible outcomes and identify the favorable ones.

Answer 1

The Correct Option is C

Step 1: The possible sums when two dice are thrown range from 2 to 12. The perfect square numbers within this range are \( 4 \) and \( 9 \). So, we need to find the probability of getting a sum of \( 4 \) or \( 9 \).
Step 2: To calculate the probability, we first determine the number of favorable outcomes for each perfect square sum:
- For a sum of \( 4 \): The possible pairs are \( (1, 3), (2, 2), (3, 1) \), which gives 3 favorable outcomes.
- For a sum of \( 9 \): The possible pairs are \( (3, 6), (4, 5), (5, 4), (6, 3) \), which gives 4 favorable outcomes.
Step 3: Total favorable outcomes for getting a perfect square sum = \( 3 + 4 = 7 \).
Step 4: The total number of possible outcomes when two dice are thrown is \( 6 \times 6 = 36 \).
Step 5: Therefore, the probability of getting a perfect square sum is: \[ P({perfect square sum}) = \frac{7}{36}. \]