# Browse Classroom Capsules and Notes

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Displaying 1 - 10 of 70

This  project uses a sampling problem to compute certain probabilities. In the process, certain binomial identities are established.

A variation of the birthday problem is being considered: what is the probabibility of $$2$$ out of $$n$$ people to have their birthday on a particular day? Furthermore, this capsule...

The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective...

The author provides a simple context and some history in which actuarial computations take place.

Consider the sum of $$n$$ random real numbers, uniformly distributed in the unit interval. Although the expected value of this sum is $$n/2$$, the value of $$n$$ for which...

The authors study the upper bound for the expected differences between order statistics of a distribution.
The probability of losing in exactly $$n$$ steps of the gambler`s ruin game is investigated.

Experiments show that people tend to behave "unfairly" in the fair R-P-S games. The authors find the optimal strategies for two cases.

The authors use a popular TV show to demonstrate probability theory.
The author proposes two extensions of the Monte Hall problem, with solutions involving the numbers $$\pi$$ and $$e$$, respectively.