Can you correct a 300-year-old error?

A challenge: can you correct something that Jacob Bernoulli got wrong? It stayed wrong for nearly 300 years until our author, Professor Antony Edwards, spotted it and corrected it.  It is a simple exercise in schoolboy probability. It is Problem XVII in Part III of Bernoulli’s book. For those who would like to try their hand, here is the problem:

http://www.significancemagazine.org/details/webexclusive/4899951/Bernoulli-and-the-Foundations-of-Statistics_-Can-you-correct-a-300-year-old-erro.html

Here are some interesting articles about Ars Conjectandi:

http://www.statisticsviews.com/details/feature/4911181/Three-Hundred-Years-of-Making-Conjectures.html
http://onlinelibrary.wiley.com/doi/10.1111/j.1740-9713.2013.00666.x/pdf