Positive Integer
Number Theory
Level
2
I have a positive integer that I'm thinking of. Now, I double the positive integer such that it becomes a new positive integer.
Which is more likely: That the new positive integer is a multiple of 3, or a multiple of 6?
They are both equally likely
Multiple of 6
Multiple of 3
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1 solution
The double of a number is a multiple of 3 if and only if that number is also a multiple of 3, and that has a probability of ⅓.
While if a number is a multiple of 3, then it's double will be a multiple of 2 × 3 = 6 .
Hence, the only requirement for both the probabilities is that the number selected should be a multiple of 3. Thus, they are equally likely.