Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?
- 5/9
- 1/36
- 1/216
- None of these
Explanation
When three 6-faced dice are thrown together, the total number of possible outcomes is 6 × 6 × 6 = 216 (since each die has 6 possible outcomes).
The favorable outcomes where all three dice show the same number are:
(1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), and (6, 6, 6)
There are 6 favorable outcomes.
The probability of all three dice showing the same number is:
Number of favorable outcomes / Total number of possible outcomes
= 6 / 216
= 1/36
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