We can use the Lindberg condition to show the distribution of number of prime divisors of an integer approaches Gaussian.

1. Is there a similar probabilistic formulation for square free numbers? That is, is it reasonable to say the probability of an uniformly random integer being square free is $\frac6{\pi^2}$ with suitable probabilistic interpretation?

2. Are there non-trivial and deceptive situations where such probabilistic interpretations break down?

We can use the Lindberg condition to show the distribution of number of prime divisors of an integer approaches Gaussian.

1. Is there a similar probabilistic formulation for square free numbers? That is, is it reasonable to say the probability of an uniformly random integer being square free is $\frac6{\pi^2}$ with suitable probability distribution?

2. Are there non-trivial and deceptive situations where such probability distribution interpretations break down?

We can use the Lindberg condition to show the distribution of number of prime divisors of an integer approaches Gaussian.

1. Is there a similar probabilistic formulation for square free numbers? That is, is it reasonable to say the probability of an uniformly random integer being square free is $\frac6{\pi^2}$ with suitable probabilistic interpretation?

2. Are there situations where such probabilistic interpretations break down?

We can use the Lindberg condition to show the distribution of number of prime divisors of an integer approaches Gaussian.

1. Is there a similar probabilistic formulation for square free numbers? That is, is it reasonable to say the probability of an uniformly random integer being square free is $\frac6{\pi^2}$ with suitable probabilistic interpretation?

2. Are there non-trivial and deceptive situations where such probabilistic interpretations break down?