I'd ask clarifying questions first:
1. Are we talking about active users of Facebook or registered users in India?
2. Are we interested in the access pattern of these users e.g. mobile or website users?
I'd assume the answer to #1 is registered users and #2 is irrespective of access pattern, we are looking at the overall number.
I'd then look at breaking the problem into manageable subsets: 1. we need to look at what's the popluation having access to internet and then 2. out of the ones having internet access, what %age of users must be using facebook.
So to solve the problem, I'd define the top level equation:
total number of FB users = # people having internet access x % of internet connected population having FB account
lets solve both of these one by one:
1. #people having internet access - since india is having huge rural population (~70%), these people are directly connecting to internet through their phones. Urban population (30%) connects to internet using both phone and computer.
70% Urban population can safely be assumed to have internet access while the rural population may be around 40%
population of India: 1.3B
#people having internet access = # rural population having internet access + # urban population having internet access
= 1300M * 70% * 60% + 1300M * 30% * 40%
= 546M + 156M
2. % of internet connected population having FB account - this one can be calculated using age/ demographics of the indian population.
Facebook has an age restriction of 13 years.
- 10% of India's population is < 13 years - can be assumed to have near zero FB accounts
- 25% of India's population is > 60 years - can be assumed to have ~25% FB accounts
- 65% of India's popluation is between 13-60 years - can be assumed to have 70% FB accounts
Now let's feed this data to our earlier equation:
% of internet connected population having FB account = 10%*0 + 25%*25% + 65%*70%
= 6.25% + 45.5%
Since we have estimate for both the key variables of our top equations for estimating the FB users in India, lets get to the final answer:
total number of FB users = 702M people having internet access x 52% of internet connected population having FB account
Now that we have our final answer, lets also assess whether this estimate seems ok or do we need to go back and correct some of our earlier assumptions.
365M out of 1300M people means 1/3 people in India using FB which to my mind is pretty reasonable number. I dont think we need to go back and correct any of our assumption. We can proceed with the estimate.