Discussion
Two unbiased dice are thrown. The probability that both dice show the same number is :
Answer: C
The probability is \(\frac{1}{6}\).
Two dice give \(6 \times 6 = 36\) equally likely outcomes. Both show the same number in exactly 6 of them: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). So
\[ P = \frac{6}{36} = \frac{1}{6} \]
Equivalently, whatever the first die shows, the second matches it with probability 1/6. The value 1/36 is the probability of one particular double, such as two sixes. The value 11/36 is the chance that at least one die shows a given number, such as at least one six, and 1/3 corresponds to no natural count here.
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