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: Recall the shortcut formula for sums with two dice.
The number of ways to get a sum $s$ with two dice is $6 - |7-s|$, valid for $2 \le s \le 12$.
Step 2: Apply it for s = 7.
\[ \text{Ways} = 6 - |7-7| = 6 \]
Step 3: Divide by the total outcomes.
\[ P(\text{sum}=7) = \frac{6}{36} \]
\[ \boxed{\frac{1}{6}} \]