# Approximating Probabilities

• Hugh Gordon
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

Sometimes an approximation is more valuable than an exact answer. For example, consider the following question: A certain association has 4000 members; 2000 of them are men and 2000 are women. Exactly half the members will be randomly chosen to each receive one ticket to a special event; all members have the same chance of getting a ticket. What is the probability that exactly 1000 men and exactly 1000 women get tickets? The answer to the question is quite obviously
$$\frac{{{{\left( {\begin{array}{*{20}{c}} {2000} \\ {1000} \end{array}} \right)}^2}}}{{\left( {\begin{array}{*{20}{c}} {4000} \\ {2000} \end{array}} \right)}}$$

## Keywords

Poisson Distribution Exact Answer Defective Item Bernoulli Trial Poisson Approximation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.