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Browse Classroom Capsules and Notes

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A collection of cards, \(r\) with red faces \(b\) with black faces, are randomly laid face down in a row. What is the probability that \(t\) cards of the same color lie consecutively?

It is known that the probability that at least two persons in a group have the same birthday, when the birthday distribution is not uniform, is no less than the probability when the...

The author computes the probability of a variation of Buffon's needle problem with uniform angular spacing.

A natural generalization of probability trees and hypergeomeric distributions is used to solve problems anti-intuitive to some.

Copulas can be employed in probability and mathematical statistics courses.

The authors describe the Hat Check and several other problems leading naturally to the number \(e\).

Dropping the smallest or largest in a finite set of numbers does not necessarily lower the variance.

A Markov chain with 9 states is used to illustrate a technique for finding the fundamental matrix.

The author shows a clever block stacking process for counting the total number of ways each possible sum can be rolled using three standard dice.

The author discusses binomial distribution where \(n\) is replaced by any positive number.