# Browse Classroom Capsules and Notes

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Displaying 11 - 20 of 70

When the sample space is too small, then Bernstein's examples on independent events fail.

Solving an expected value problem without using geometric series

In the game of tennis, if the probability that player $A$ wins a point against player $B$ is a constant value $p$, then the probability that $A$ will win a game from deuce is \(p^2/(1 - 2p...

The authors give two proofs, one geometric and one algebraic, to provide insight into why the sum of independent normal. random variables must be normal.

A solution to a probabilistic Putnam Exam Problem is presented.

This article links two seemingly unrelated problems, one in probability and the other in dynamical systems, and shows they are actually one involving Fibonacci numbers.

Probabilistic analysis of the importance of a game in a series of games in a competition

The author derives approximations for the probability arising in birthday-type problems without using calculus.

The author applies basic probability theory to the papal election of 1458.

The authors give a "simple, conceptual" proof of the fact that the t-distribution converges to the standard normal. The proof is accessible to undergraduates.