### Declan Stacy

Math (Spring 2020 - Spring 2021), dstacy10@stuy.edu

**Problem Solving**

### A Combinatorial Identity

*by Declan Stacy*| March 2021

Let S be the set of n-tuples A=(a_1, a_2, ..., a_n) such that a_i >=0. A summation question and solution.

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### Friends Problem

*by Declan Stacy*| Feb 2021

A presentation of a solution and generalization of the friends problem through the use of random variables, probability distributions, and expectation.

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### Marbles

*by Declan Stacy*| Feb 2021

Johnny has a bag of marbles with n red marbles and n blue marbles. What is the probability that he goes through the entire bag before stopping?

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### Conditional Probability

*by Declan Stacy*| June 2020

An introduction to conditional probability and the most important theorems relating to it. At the end, there are interesting problems to try and solutions.

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### Conditional Probability Problem Set

*by Declan Stacy*| June 2020

Solutions to the Conditional Probability Problem Set

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