If you randomly choose one of the first 12 prime numbers, what is the probability of choosing a prime number less than 20?

Example Answer

Assuming each of the first 12 primes is equally likely, the probability is 8/12 = 2/3, about 66.7%. The first 12 primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37. The first eight of those are less than 20.

Why this works

The sample space is the first 12 prime numbers, not the integers from one to 12 or one to 20. One is not prime. With unequal selection probabilities, I would add the probabilities assigned to the eight qualifying primes instead of dividing counts.