Assuming everything else being the same, which Startup has a higher
chance of success; the one that targets one source of revenue or the
one that projects the same total profit but through multiple sources
of revenues?

The results are the same (i.e. Expected return).  What is different
would be the standard deviation.  If the multiple revenue sources are
independant of one another, it would likely be safer (i.e. more likely
to get that expected return).
Think of it as being similar to investing in one stock verse investing
in many.  Investing in many (diversifying) is safer (because a loss
peculiar to a single stock would not effect the portions attributed to
other stocks), but it does not increase your expected return.  Also,
diversification may limit loss, it liekwise limits upside.  So keep
that in mind to.

In sum, the cnaces are the same.

Well, I am not sure if we can compare that with stock diversification.
In case of startups you have human factors involved. You can have all 
your sales/marketing staff going after one revenue source, or spread them 
around multiple sources. From pure mathematical point of view it 
may increase the chance of making ?any revenue? at all, but I am 
wondering if it would increase the chance of successful growth for a company!

Excellent comments from both. My 2 cents are these.

1. By sources, do you mean 3 different products lines, 3 different
manufacturing processes, 3 diff. business lines.  This is way more
difficult to do if you are a FIRST time startup entrepreneur.   If
they are SIMILAR to each other, that is anther story.

2. If you mean 1 product to 3 markets, I would suggest concentrating
on 1 market (the one most familliar/studied/researched) and it NOT
need be the biggest in terms of money.

Bottom line, do you want to be a BIG fish in a SMALL pond or a SMALL
fish in a BIG pond.  You should answer that honestly first.  My advice
would be being a BIG fish in a small pond, concentrate resources,
become an expert in this market, build a reputation, clients,
testimonials before you tackle a new (not new product) market.

Hope that helps.