Key points Listing outcomes to find the probability of combined events Examples Questions Using sample space diagrams to find the probability of combined events Examples Question Taking a logical and ...

The sample space diagram shows there are 6 ways of making a 7, out of a total of 36 possible outcomes. Therefore, the probability of rolling two dice and the sum being 7 is \(\frac{6}{36} = \frac{1}{6 ...

This is a preview. Log in through your library . Abstract We prove that if (X, A, P) is an arbitrary probability space with countably generated σ-algebra A, (Y, B, Q ...

Many other planets throughout the universe probably hosted intelligent life long before Earth did, a new study suggests. The probability of a civilization developing on a potentially habitable alien ...

Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

A generalization of the Shannon-McMillan Theorem ($L^1$ version) is obtained for the action of an amenable group on a probability space, thereby settling a conjecture ...

This article was originally published at The Conversation. The publication contributed the article to Space.com's Expert Voices: Op-Ed & Insights I was preparing for my early morning class back in ...

This paper presents an analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations. Considering the first to be subjected to a ...