Browse Classroom Capsules and Notes

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Child's Play

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.

Poker with Wild Cards-A Paradox?

Allowing use of wild cards in poker can lead to unresolvable inconsistencies.

General Russian Roulette

The game of Russian roulette is generalized to \(n\) players, each with a revolver.

Probabilities of Clumps in a Binary Sequence

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?

Buffon's Needle Problem on Radial Lines

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

Majorization and the Birthday Inequality

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...

Time-Sharing and the DeMoivre-Laplace Theorem

The author discusses an application of the Central Limit Theorem.

Math Bite: The Dagwood Random Nap

An old Dagwood cartoon introduces brief discussion of a simple problem involving random walks.

Bernoulli Trials and Family Planning

The expected waiting time for \(n\) successes and \(m\) failures in Bernoulli trials is calculated in two different, but complementary, ways.

The Poisson Variation of Montmort's Matching Problem

A generalization of the classical hat-check problem is introduced and solved.