Question

If two dice are rolled simultaneously, then the probability that the difference of the numbers on the two dice equals to zero is

• A. \( \frac{1}{12} \)
• B. \( \frac{1}{9} \)
• C. \( \frac{5}{36} \)
• D. \( \frac{7}{36} \)
• E. \( \frac{1}{6} \)

Hint:

For probability problems, always count the total possible outcomes and favorable cases separately.

Answer 1

Answer: (E)

Step 1: Total Outcomes When rolling two dice, there are: \[ 6 \times 6 = 36 \] total possible outcomes. 
Step 2: Favorable Cases The difference of the numbers is zero when both dice show the same number. The valid cases are: \[ (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) \] So there are \( 6 \) favorable outcomes. 
Step 3: Compute Probability \[ P = \frac{{favorable outcomes}}{{total outcomes}} = \frac{6}{36} = \frac{1}{6} \]
Final Answer: \[ \boxed{\frac{1}{6}} \]