Question

Two dice are thrown simultaneously. The probability of getting a sum of 7 is :

• A. \(\frac{2}{9}\)
• B. \(\frac{1}{9}\)
• C. \(\frac{5}{36}\)
• D. \(\frac{1}{6}\)

Hint:

A sum of 7 is the most likely sum when rolling two dice because it has the maximum number of favorable combinations (6 out of 36).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Two standard six-sided dice are rolled. We need to find the probability that the sum of the numbers showing on both dice is equal to 7.

Step 2: Key Formula or Approach:
- When two dice are rolled, the total number of outcomes is \(6 \times 6 = 36\).
- Let \(E\) be the event that the sum of the outcomes is 7. We count the outcomes \((x, y)\) such that \(x + y = 7\).

Step 3: Detailed Explanation:

• List the favorable pairs \((x, y)\) where \(x, y \in \{1, 2, 3, 4, 5, 6\}\) and \(x + y = 7\):
- \((1, 6)\)
- \((2, 5)\)
- \((3, 4)\)
- \((4, 3)\)
- \((5, 2)\)
- \((6, 1)\)

• Count the number of favorable outcomes:
There are 6 favorable outcomes.

• Apply the probability formula:
\[ P(\text{sum is 7}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{6}{36} \]

• Simplify the fraction:
\[ P(\text{sum is 7}) = \frac{1}{6} \]


Step 4: Final Answer:
The probability of getting a sum of 7 is \(\frac{1}{6}\).