The Probability of Relatively Prime Numbers - A Mathematical Analysis

Explore a 19-minute mathematical video that delves into the fascinating probability problem of determining whether two randomly selected integers are relatively prime. Learn essential concepts including probability laws, infinite series, and the Basel problem while discovering how to calculate the likelihood of numbers sharing common factors. Through step-by-step explanations, master the law of complement, joint probability, infinite products, and ultimately find the solution to this intriguing mathematical puzzle. Gain insights into the sum of reciprocal squares and the Riemann zeta function at s=2, building a deeper understanding of number theory and probability concepts.