Chance events are very common in our daily lives. Everyday, we face situations where the result is uncertain, and maybe, without realizing it, we guess the likelihood of one outcome or another. You hear such words from daily conversation all the time: 'the chances, I guess, are...', 'the odd against...'. As you may see from the activities below, even some simple and elementary probability can cast new light on situations where randomness and chance appear to rule.

In the following activities, first we will review some basic concepts in Permutation and Combination, then we'll introduce bionomial distribution and Poisson distribution, and if you pay some attention, you'll see these distributions occur in daily life vrey often. Then we'll discuss the Birthday Problem, this is a great example that elementary probability can sometimes give quite surprising results. Next we'll go on to conditional probability and explore the famous Monty Hall Problem. Finally, we'll discuss Bayes' Formula and see some applications.

• • Permutations and Combinations
  • Binomial, Multinomial and Poisson Distribution
  • Birthday Problem
  • Conditional Probablity and Monty Hall Problem
  • Bayes' Formula
  • References

The Math Explorers' Club materials come in independent self-contained sections, called modules. Each module teaches material associated with a particular theme and is aimed at students with a particular level of mathematical sophistication. This website is one such module. Please see the main Math Explorers' Club website for a list of all of the modules.

This work is made possible by NSF grant.