Question

Three dice are thrown simultaneously. The probability that all the three outcomes are the same number, is:

• A. \( \frac{1}{6} \)
• B. \( \frac{1}{216} \)
• C. \( \frac{1}{72} \)
• D. \( \frac{1}{36} \)
• E. \( \frac{5}{36} \)

Hint:

When calculating probabilities, the total number of outcomes is the product of the number of possible outcomes for each event. The probability is the ratio of favorable outcomes to total outcomes.

Answer 1

The Correct Option is D

When three dice are thrown, each die has 6 possible outcomes. Therefore, the total number of possible outcomes when throwing three dice is: \[ 6 \times 6 \times 6 = 216. \] For all three dice to show the same number, there are only 6 favorable outcomes, one for each number on the die (i.e., all three dice showing 1, all three showing 2, etc.).
Thus, the probability of all three dice showing the same number is the ratio of favorable outcomes to total outcomes:
\[ P(\text{same number on all three dice}) = \frac{6}{216} = \frac{1}{36}. \]
Thus, the correct answer is option (D).