Meeting a lovely CHARGE family

By chance, someone at our church was taking with one of their work mates and found out that they had a child with CHARGE syndrome over 10 years ago. Unfortunately the child only lived four months but he has left a lasting memory with the family.

Today we were blessed with the opportunity of meeting with the family. They were lovely and showed us an album of photos that they had of their child. We talked for hours and we look forward to an oportunity to see them again.

I believe that the probability of knowing someone, who knows someone that has CHARGE syndrome are quite high. If I assume that I know one hundred people and each of those people knows another one hundred unique people then I calculate there to be 64% chance that one of those people will have charge syndrome. Calculated as follows

n=assumed number of unique people an individual person knows
=100

c=assumed chance of having CHARGE syndrome
=1/10,000

h=chance of knowing at least one person who has CHARGE syndrome
=sum[i=1 to 100] c*(1-c)^(i-1)

k=chance of knowing at least one person who knows at least one person has CHARGE syndrome
=(sum[i=1 to 100] h*(1-h)^(i-1))+h

I hope you can forgive my make-do mathematics without access to the necessary symbols and positioning.