Forbes contributors publish independent expert analyses and insights. Writes about the future of finance and technology, follow for more. Joint probability teaches us to calculate combined outcomes.

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

Stephen Woodcock does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

The mathematician Daniel Litt has driven social media users to distraction with a series of simple-seeming but counterintuitive probability puzzles. In late January, Daniel Litt posed an innocent ...

Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...