What is the probability of choosing a prime number?

Although there are infinitely many primes, they become rarer and rarer so that as the number of numbers increases, the probability that picking one of them at random is a Prime number tends to zero*.

In the first 10 numbers there are 4 primes, so the probability of picking one is 4/10 = 2/5 = 0.4

In the first 100 numbers there are 26 primes, so the probability of picking one is 25/100 = 1/4 = 0.25

In the first 1,000 numbers there are 169 primes, so the probability of picking one is 168/1000 = 0.168

In the first 10,000 numbers there are 1,229 primes, so the probability of picking one is 0.1229

In the first 100,000 numbers there are 9592 primes, so the probability of picking one is 0.09592

In the first 1,000,000 numbers there are 78,498 primes, so the probability of picking one is 0.078498

In the first 10,000,000 numbers there are 664,579 primes, so the probability of picking one is 0.0664579

* Given any small value ε less than 1 and greater than 0, it is possible to find a number n such that the probability of picking a prime at random from the numbers 1-n is less than the given small value ε.