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Thanks.
As you say, a range is the only way of providing 'certainty' but I think assumptions can be made as I have done in my previous post. It's safe to say that (most) adults in the UK have a FB account and so this total available audience can be used as a proxy for total addressable audience size. I guess this would be better if we were running TV as who doesn't have one of those but we're not...
If we do make that assumption that everyone who has a Twitter & LinkedIn account (and if we add more channels like newspapers, magazines etc etc) has a FB account then can I narrow down the range for more than two channels?
Soul-
If we do make that assumption that everyone who has a Twitter & LinkedIn account (and if we add more channels like newspapers, magazines etc etc) has a FB account then can I narrow down the range for more than two channels?
As in your post if you assume that probability of hitting a person on one platform is independent of whether you hit them on another platform, it's just like a binomial distribution with multiple p values. I'm out walking so I don't have a pen or anything but I think in your example you'd have P(X ≥ 1) = 1 - P(X = 0) = 1 - (6/12) × (9/12) × (9.6/12) = 70% where X is the number of platforms you reach someone on.
frankenbike
Not sure you can do any better than a min/max range on this without knowing at least something about the crossover in accounts at the least. e.g. the 12m Facebook users could be completely distinct from the 6m LinkedIn or one group could be a subset of the others.
Worst case scenario is that all your reached people are the same i.e. the 3m LI and 2.4m Twitter are just subsets of the 6m FB and all unreached users are distinct: you've reached 6/(12+1+3.6) = 38.9%. Best case scenario: the reverse, all your reached people are distinct and the overlap in accounts is 100%, i.e. (6+3+2.4)/12 = 95%.
Other than that you have to make assumptions - in your calculation it looks like you've assumed all LinkedIn users have a Facebook account and your probability of reaching them on one platform is independent of whether you reached them on the other.