Friday, October 16th at 4:00pm in Kerchof Hall 317 (pizza arrives at 3:45)
Speaker: Prof. Gregory Arone (UVa Department of Mathematics)
Title: Some improbable probabilities

Abstract: A new family just moved in to your neighborhood. You were told that they have two children, at least one of whom is a girl. What is the probability that both children are girls?

The answer to this is obvious. The gender of one child has no bearing on the gender of another, so the probability that the other child is a girl, and so both children are girls, is 1/2.

But wait. There is a different answer, that is equally obvious. There are four possibilities for a family with two children: GG, GB, BG, BB. There are twice as many families with one boy and one girl than families with two girls. If you know that one of the children is a girl, then you are left three equal possibilities: GG, GB, and BG. Only in one out of three cases will the other child turn out to be a girl. It follows that the probability is 1/3! So which answer is right?

Probability is a central subject in mathematics and its applications. The methods of probability are successfully used in science, engineering, etc. Yet, it is exceptionally easy to commit a logical fallacy when dealing with probabilities. We will examine several elementary probability problems that have "paradoxical" or "counterintuitive" answers. No mathematical background beyond high school will be assumed.