Abstract: We review the recent progress on the definition of randomness with respect to conditional probabilities and a generalization of van Lambalgen theorem (Takahashi 2006, 2008, 2009, 2011). In ...

Possibility theory and conditional probability offer complementary perspectives for modelling uncertainty, with each framework contributing distinct advantages. Possibility theory, rooted in fuzzy set ...

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 ...

Take two events A and B. For example, let A be the event “Receive a score of 95% on the econometrics exam” and let B be the event “Study econometrics 12 hours a day”. We might be interested in the ...

ABSTRACT: We elaborate on an alternative representation of conditional probability to the usual tree diagram. We term the representation “turtleback diagram” for its resemblance to the pattern on ...

The probability that a tennis player wins the first set of a match is \(\frac{3}{5}\). If she wins the first set, the probability that she wins the second set is \(\frac{9}{10}\). If she loses the ...