InterviewSolution
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InterviewSolution
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If two distinct numbers m and n are chosen at random form the set {1, 2, 3, …, 100}, then find the probability that `2^(m) + 2^(n) + 1` is divisible by 3. |
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Answer» Correct Answer - `(49)/(198)` `2^(m) + 2^(n) + 1 = (3 - 1)^(m) + (3 - 1)^(n) + 1` `=3k + (-1)^(m) + (-1)^(n) + 1` This is divisible by 3 if both m and n are even. `therefore` Required probabaility = `(.^(50)C_(2))/(.^(100)C_(2)) = (50 xx 49)/(100 xx 99) = (49)/(198)` |
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