Conditional probability occurs when it is given that something has happened. (Hint: look for the word “given” in the question. The probability that a tennis player wins the first set of a match is ...

Author: Chris Boucher (March 2011). This app displays an intricate Venn diagram, containing various combinations of set intersections, unions and complements. Users can shade the area they choose by ...

"Yes or no: was there once life on Mars?" I can't say. "What about intelligent life?"' That seems most unlikely, but again, I can't really say. The simple yes-or-no framework has no place for shadings ...

There is no set Δ of probability axioms that meets the following three desiderata: (1) Δ is vindicated by a Dutch book theorem; (2) Δ does not imply regularity (and thus allows, among other things, ...

Let $(X, \mathscr{A}, P)$ be a probability space and $\mathscr{B}$ a sub-$\sigma$-algebra of $\mathscr{A}$. Some results on regular conditional probabilities given $\mathscr{B}$ are proved. Using ...