M245.pdf

The M500 Society is a mathematical society for students, staff, and friends of the Open University, aiming to promote a better understanding of mathematics through publishing the magazine M500 and organizing residential weekends. The magazine provides a forum for readers' mathematical interests, and contributions are welcome on virtually anything related to mathematics. An article discusses a problem involving two tins of biscuits, where a biscuit is taken from a randomly chosen tin until one tin is empty, and the expected number of biscuits remaining in the other tin is calculated using a modified version of the negative binomial distribution. The problem is extended to two tins with different numbers of biscuits and to three tins, and challenge problems are posed, including finding the expected number of biscuits remaining in the third tin when the other two tins have been emptied. Another problem involves a dinner club where the bill needs to be settled when two birthday meals are combined into one.