# Browse Classroom Capsules and Notes

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Displaying 61 - 70 of 70

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.

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... Solving an expected value problem without using geometric series When the sample space is too small, then Bernstein's examples on independent events fail. The author proposes two extensions of the Monte Hall problem, with solutions involving the numbers \(\pi$ and $e$, respectively.
The authors use a popular TV show to demonstrate probability theory.

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 probability of losing in exactly $n$ steps of the gambler`s ruin game is investigated.
The authors study the upper bound for the expected differences between order statistics of a distribution.
Some probalistic examples, primarily in the game of bridge, not found in standard elementary texts, are discussed.