Final answer:
The probability of being relatively prime refers to the likelihood that two numbers have no common factors other than 1. Euler's totient function is used to calculate this probability. The numbers 21 and 35, for example, are not relatively prime as their greatest common divisor is 7.
Step-by-step explanation:
The probability of being relatively prime refers to the likelihood that two numbers have no common factors other than 1. For example, if we consider two randomly selected numbers, the probability that they are relatively prime is related to the concept of the Euler's totient function.
Euler's totient function φ(n) gives the count of integers from 1 to n (inclusive) that are relatively prime to n. The probability of two randomly selected numbers being relatively prime is given by:
P(relatively prime) = φ(n) / n^2
For example, if we consider the numbers 21 and 35, their greatest common divisor (GCD) is 7. Since the GCD is not 1, the numbers are not relatively prime. Therefore, the probability of being relatively prime for these numbers would be 0.