Correct : 0.0277

When three fair dice are thrown simultaneously, we need to find the probability that all three show the same number.

A fair die has 6 possible outcomes (1, 2, 3, 4, 5, 6).
When three dice are thrown together, the total number of possible outcomes is:
6 × 6 × 6 = 216

Now let me count the favorable outcomes where all three dice show the same number:
(1, 1, 1) - all three show 1
(2, 2, 2) - all three show 2
(3, 3, 3) - all three show 3
(4, 4, 4) - all three show 4
(5, 5, 5) - all three show 5
(6, 6, 6) - all three show 6

So there are 6 favorable outcomes.

The probability is calculated as:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 6/216
Probability = 1/36
Probability = 0.027777...

Rounding to three decimal places:
Answer: 0.028 (or 0.027)