A probability questions with a few factors (pure curiosity, not homework)

Question

What is the probability of two people who were born in different states (let’s call them N and C) having the same birthday (June 10) and their mothers also have the same birthday (January 13). Furthermore, what are the chances of that happening AND they end up meeting and becoming friends? Do the odds increase and make it less likely with the factor of them meeting?

Answer 1

1/365)^2 = probability of both same birthdates

= 1/(365)^2 = 7.5 x 10^-6

= .0000075= 0.00075% chance

chances of meeting and becoming friends makes the odds far more unlikely