Discussion
A die is rolled once. If the die shows odd number, then the probability of getting other than 5 is
Answer: D
The probability is \(\frac{2}{3}\).
Given that the die shows an odd number, the outcomes are reduced to {1, 3, 5}, all equally likely. 'Other than 5' leaves {1, 3}:
\[ P = \frac{2}{3} \]
As a conditional probability, \(P(\text{not 5} \mid \text{odd})\) is \(\frac{P(\{1, 3\})}{P(\text{odd})} = \frac{2/6}{3/6}\). \(\frac{5}{6}\) ignores the condition, and \(\frac{1}{3}\) is the probability of getting 5.
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