<p>Three identical dice are rolled. The probability that the same number will appear on each of them is</p>
<p>(a) \(\frac{1}{6}\)</p>
<p>(b) \(\frac{1}{36}\)</p>
<p>(c) \(\frac{1}{18}\)</p>
<p>(d) \(\frac{1}{28}\)</p>
Step-by-Step Solution
Key Concept: When rolling three identical dice independently, each die has 6 possible outcomes. The favorable outcomes are only those where all three dice show the same value (1,1,1), (2,2,2), ..., (6,6,6). Use the multiplication rule: P(same on all three) = (number of favorable outcomes)/(total outcomes).
<p><strong>Step 1:</strong> Total possible outcomes when rolling three dice = 6 × 6 × 6 = 216</p><p><strong>Step 2:</strong> Favorable outcomes (all three dice show the same number) = (1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5), (6,6,6) = 6 outcomes</p><p><strong>Step 3:</strong> Probability = Favorable outcomes / Total outcomes = 6/216 = 1/36</p><p>∴ Answer: B (which is 1/36)</p>
Correct Answer: B