I had no idea Ravi Shankar is the father. WOW! Offcourse, Ravi turns out to be a poor excuse of a father and Norah had no real connection to her Bangali roots. I only found out about this connection as I was looking up Arnob's music in youtube, landed into related links that lead me to Anoushka Shankar's songs and a collaboration between Anoushka Shankar & Norah Jones. One of the comment mentioned that they were half sisters. jumped to imdb to find this:
http://www.imdb.com/name/nm1289528/bio
Gotta love the internet.