If you know that one child in a two-child family is a boy, what is the probability that the other child is also a boy? What is the chance that a random chord in a circle is longer that the radius? How many people di there have to be in a room before it is more likely than not that two of them will have the same birthday?
Paradoxes, like the famous examples above, seem to turn up in probability more than any other area of Mathematics. This talk will discuss further examples, and then show how the birthday paradox has applications to finding factors of large integers, and to cryptography.
Joe Buhler has taught at Reed College, Harvard University, and Penn State. Currently, he is the Deputy Director at the Mathematical Sciences Research Institute in Berkeley. He has workedin a number of areas of mathematics, including number theory, combinatorics, algebra, computation, and the mathmatics of juggling patterns.