If the odds, or the genes, are to be believed, then the newly born daughter to the Bachchan-Rais is destined for the silver screen.
She might only be in the first week of her life, but being born into Bollywood royalty gives her a head start like no other.
Her mother is Aishwarya Rai, the face of L'Oreal, a former Miss World, who has starred in a number of Bollywood films.
Her father is Abhishek Bachchan, a Bollywood actor who is rarely far from the front pages of magazines.
Her grandmother is actress Jaya Bhaduri. And her grandfather is India's most famous man, Amitabh Bachchan, a Bollywood megastar whose career has spanned decades.
Blood is thick in Bollywood.
There are eight-to-10 prominent families who control at least 65% of the Indian film industry, says SMM Ausaja, a Bollywood historian and author.
The vast majority of the country's top acting talent is from a so-called "filmi" family, of either actors or producers.
Salman Khan, Kareena and Karishma Kapoor, Saif Ali Khan, Ranbir Kapoor, Hrithik Roshan, Sanjay Dutt and Bobby and Sunny Deol are just some of the star names belonging to powerful Bollywood families.Rise of the Kapoors
This genetic dominance began in the 1940s, when the old Bollywood studio system broke down says Ausaja.
Like the collapse of Hollywood star system, it meant film studios were no longer contracted to hire certain actors or manage their careers and paved the way for independent producers.
"The family element really came in because the producer preferred his own son to come in rather than somebody else," says Ausaja.
The beginnings of the biggest and most feted Bollywood family date from around this time, when actor and producer Prithviraj Kapoor helped launch his sons Raj, Shashi and Shammi Kapoor.
Raj Kapoor, who went on to become the most successful of the trio, later set up his own studio to launch the careers of the next generation of his family members, including his son, Randhir.
The big budget film Rockstar, which opened this week in India, stars the youngest of the Kapoor acting clan, Ranbir Kapoor.
"Yes I come from a film family and I've been brought up in a very cushioned environment, but I'm a working professional.
"I take credit for my success and I deal with my failures and I think that just makes you more mature as a person," he says.
Kapoor, who is one of Bollywood's men of the moment, told the BBC that being from a dynasty didn't protect him from the challenges of the industry: "It's a jungle and you have to make a name for yourself," he said.Family business
Of course having a big name, makes it easier.
This is also true in Hollywood which is home to acting dynasties such as the Redgraves, the Sheens, the Douglases and the Fondas, but Indian culture is a big reason why a few families dominate.
"There's a lot of loyalty value to a family name," says Ausaja.
"Indians are emotional people and are film crazy, if they like an actor such as Amitabh, they'll pass on that love to their son or daughter."
It's also traditional in India for a trade or profession to be passed on to the next generation.
"It's like passing down a jewellery business or something. It's almost assumed the son will go into that, and take the mantle further," says Yogesh Roy, the son of Nirupama Roy, who starred alongside Amitabh Bachchan in a number of films in the 1970s and 1980s.
For Roy there was a certain sense of expectation he would become an actor, borne out of a childhood growing up on film sets.
"We were always exposed to the screen life, I used to go with my mother for shoots and I would rehearse with her and we'd go through scripts. I even dubbed some of the children's part," he recalls.
Despite all this encouragement Roy decided he was too shy to follow in his mother's footsteps but stayed in the industry as a designer to many film stars.
But taking the family business also makes a lot of practical sense to many of the children who are brought up in such an environment.
"It helps you understand what's expected you of a professional. Things that outsiders learn along the way are already given to us from our parents," says director Rohan Sippy, the son of acclaimed director Ramesh Sippy, who directed the 1970s Bollywood classic, Sholay.
"It does give you a certain equity and goodwill over a complete newcomer, but after your break you still have to have the talent to sustain it," he says.Nostalgia
Of course there are some who can break through without the help of a dynasty. One of Bollywood's biggest stars Shah Rukh Khan is not a member of any film clan.
"SRK broke through out of sheer luck and energy that he possesses and that he got the right time.
"You can have more flops and take risks if you are the child of a prominent star," says Ausaja.
Sippy says the industry is now changing, with more actors and producers from a non-film background entering the profession.
But Ausaja believe the dynasties will still reign in Bollywood for years to come because it's what the fans want.
"I don't see that loyalty breaking. People connect with nostalgia and their favourite star, and that carries down to generations of filmgoers."